Physics II - Test 3

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•On the diagram, draw two rays from the top of the candle: 1.Approaching the mirror through C 2.Approaching the mirror parallel to the principal axis

(pic)

A pencil sits in front of a convex mirror with incident and reflected rays traced from the pencil tip. In the previous question featuring the convex mirror, what is the approximate focal length f?

-1.5 cm The focus is at a position of 4.5 cm. The mirror is at a position of 6 cm. The distance from the focus to the mirror will be f = 4.5 c m − 6 c m = − 1.5 c mf = 4.5 c m − 6 c m = − 1.5 c m. I wrote this so that it's clear that the focal length is negative, but even if I hadn't written the subtraction in that order, we have to make the focal length negative for a convex mirror (always).

The magnetic flux through this loop increases as it enters this uniform external magnetic field. What happens? According to what?

-According to Lenz's Law, the loop will try to oppose this increase in flux. The opposite of "more" is "less." -The only tool it possesses to lessen the flux is the ability to create its own magnetic field to try to cancel out the external field that points into the screen. -It creates its own magnetic field that points out of the screen.

Determine whether each loop will develop a clockwise, counterclockwise, or no current based on its motion Vertical wire with current flowing up -Magnetic Field into screen on right, out of screen on left Loop A flows up parallel to wire Loop B Flows left away from wire Loop C flows right away from wire If loop moving away to regions of weaker external magnetic field (pic)

-Magnetic Field strongest closest to wire üWith wire loops, it's easiest to use RHR2 with your thumb as the magnetic field inside the loop. üYour fingers will bend to show you the currents that created the field. üLoop B must have developed a CCW current because its field points out of the screen. üLoop C must have developed a CW current because its field points into the screen.

Loop of wire moves to the right into a magnetic field pointing into screen. What kind of current must be created in this wire to induce this outward magnetic field?

-Only a CCW current could've made this induced field. -The direction of the current comes from the special version of RHR2 (most useful for loops of wire; thumb is the magnetic field inside the loop, fingers bend as current).

-The Mirror Equation predicts that d_i=(-1.5 cm) -This minus sign means that the image will appear to be located 1.5 cm ______ the mirror.

-The Mirror Equation predicts that d_i=▭(-1.5 cm) -This minus sign means that the image will appear to be located 1.5 cm behind the mirror. -It will appear as if you would have to reach your hand "through" the mirror to touch the image you see.

For a lens is the object distance positive or negative? Explain

-The object distance is positive because it's in front of the lens, and generally, it would make no sense to ever call the object distance negative, because you could always just turn the lens around and say that the object is in front of the lens

-We know it's a __1___ image because _____1_____ light rays converge to one spot, at the image's location -Because _______ light rays converge on a single location, this image could be projected onto a screen

-We know it's a real image because real/actual light rays converge to one spot, at the image's location -Because real light rays converge on a single location, this image could be projected onto a screen -It's also inverted, which is another clue that it's real.

-We know it's a __1___ image because there are no __2____ light rays converging to one point in space - merely the appearance that they diverged from behind the mirror. -It's also upright, which is another clue that the image is ___2___. -Convex mirrors only make smaller, upright, ___1____images.

-We know it's a virtual image because there are no real light rays converging to one point in space - merely the appearance that they diverged from behind the mirror. -It's also upright, which is another clue that the image is virtual. -Convex mirrors only make smaller, upright, virtual images.

-While the __1____ is changing, current flows through a circuit with no voltage source. -How the __1____ through the loop changes is not important. -If ___1___ through the loop changes (in any way), the wire loop creates ___2____ to ___3___ any change to its present ___1____. - What Law is this?

-While the flux ΦB is changing, current flows through a circuit with no voltage source. -How the flux through the loop changes is not important. -If Φ_B through the loop changes (in any way), the wire loop creates its own new magnetic field to directly oppose any change to its present Φ_B. Lenz's Law

What is faraday's law of induction

-magnetic fields that change over time they create their own electric fields -electrodynamic fields only exist while a magnetic field changes it can change in strength it can change in direction or both but you won't see this happen if a magnetic field is static if nothing about the magnetic field changes you won't induce electrodynamic fields. electrodynamic fields are they are actual electric fields they're real electric fields but they're not made by individual electric charges so their field lines don't have a beginning or an end they don't emanate out of positive charges and terminate into negative charges they're not made from electric charges they're created entirely dynamically by time-changing magnetic fields and so they just like magnetic fields make continuous loops they point in exactly the direction that the induced current flows according to lenz's law.

What are the two reasons that you could see the same induced current flow when you change magnetic flux through a coil of wire. Explain.

1. Induced currents can flow when you physically move/reshape the wire in/near a magnetic Field (B). For example, dragging the wire loop into or out of an external magnetic field. This is called Motional Electromotive Force (Motional EMF), because the wire's motion is required. 2. Induced current can flow due to Faraday's Law. This requires no motion from the wire loop itself. This is a purely electromagnetic law of nature that illustrates symmetry of electric and magnetic fields.

•On the diagram, draw two rays from the top of the candle through the lens. Real or virtual?

1.Approaching the lens through C 2.Approaching the lens parallel to the principal axis •We know it's a real image because actual light rays converge to one spot in real space. •The rays do not appear to diverge from somewhere •Remember, real images: •Are always inverted •Only appear on the real side of the lens (the back side, where light actually goes) •Can be aimed/projected onto a screen

In which direction will a current flow through this loop as it exits the magnetic field? magnetic field points out of screen

1.Does the flux change? If so, how? Yes, the flux changed from all positive (cos⁡〖0°〗=1) to all negative (cos⁡〖180°〗=-1). 2.How will the loop of wire respond to this change? The wire will respond by opposing the loss of positive flux/gain of negative flux. To do this, it must make more positive flux to try to maintain its status before the change. That means induce a magnetic field that points out of the screen to create more positive flux. 3.In which direction would a current need to flow to create this response? To create more magnetic field that points out of the screen, the wire must make a counterclockwise current according to RHR2. thumb out of screen fingers to left

A magnetic field pointing out of the screen moves away from a wire loop. In which direction will a current flow through this loop as it exits the magnetic field?

1.Does the flux change? If so, how? Yes, the flux through the area enclosed by this wire loop disappears. 2.How will the loop of wire respond to this change? The wire will respond by opposing this loss of flux, which means it will have to make more. That means induce a magnetic field that points out of the screen to compensate for what's lost. 3.In which direction would a current need to flow to create this response? To create more magnetic field that points out of the screen, the wire must make a counterclockwise current according to RHR2. Thumb out of screen fingers to left

1.________ images can be projected onto screens (because they're created by real light rays that can be aimed at a wall) 2._______ images are always inverted.

1.Real images can be projected onto screens (because they're created by real light rays that can be aimed at a wall) 2.Real images are always inverted.

Diverging Lenses 1.They never converge light to a single point on the ____1____ side of the lens; they only diverge it out the ____2____ side.

1.They never converge light to a single point on the real side of the lens; they only diverge it out the back side.

mirror equation is

1/f = 1/do + 1/di

A pencil sits in front of a convex mirror with incident and reflected rays traced from the pencil tip. What is the approximate object distance d o in this scenario?

2 cm The object is at a position of 8 cm. The mirror is at a position of 6 cm. The distance from the object to the mirror will be d o = 8 c m − 6 c m = 2 c md o = 8 c m − 6 c m = 2 c m.

Radio waves occupy the frequency range from _____ Hz up to about ______ Hz (______kHz).

30 Hz up to about 30 000 Hz (30 kHz).

The distance between peaks in the electric field for a certain shade of blue light is about 460 nanometers (nano = 10 − 9). If this EM wave impacted your retina, how many complete wave cycles would be interacting with your eye each second?

6.5 × 10 14 waves per second That's a lot of complete waves per second.

A loop of wire generates ______ to oppose any change in magnetic flux ΦB that it experiences. What Law is this?

A loop of wire generates its own new magnetic field B _induced to oppose any change in magnetic flux ΦB that it experiences. Lenz's Law

A stationary wire loop is exposed to a bar magnet that is gradually moved closer to the wire. which of the following best explains the reason that an induced current would flow in the wire loop?

A magnetic field that changed its strength over time induces an electric field that pushes the charges into motion

In _____, the charges move back and forth many times per second, without ever traveling around the entire current. What does it make?

Alternating Current Because current switches signs many times per second, the charges in the wire must accelerate and decelerate endlessly so alternating current makes time-varying E and B fields

As shown in the Pre-Lecture video, the rate at which the magnetic flux Φ B through a loop of wire changes determines the size of the induced voltage ΔV Induced in the wire. This induced voltage compels the current to flow. ΔVInduced = − ΔΦB/Δt According to this relationship, and without worrying about the minus sign (which we'll explain later), the ["smaller", "larger"] the change in magnetic flux and the ["shorter", "longer"] the duration that it changes, the larger the induced voltage will be. This will cause the biggest induced current to flow.

Answer 1:larger Answer 2:shorter The more you change the flux (and the more quickly you change it), the larger the induced voltage will be, which will produce a bigger induced current.

Any Ray that approaches the lens ______ to the principal axis refracts out through the back focus F in converging lenses

Any Ray that approaches the lens parallel to the principal access refracts out through the back focus F in converging lenses

**A stationary rectangular loop of wire rests below a long, straight, current-carrying wire as seen below. Current in the long wire moves to the RIGHT. In which direction would we need to move the loop to induce a CLOCKWISE current?

Away from the wire If the goal is to create a CLOCKWISE current in the loop of wire, then this would ultimately create an induced magnetic field that points into the page within the interior of the rectangular wire loop. What would we need to do to create an induced -field pointing into the page? We could either (A.) move the loop to a region where less inward-pointing magnetic flux exists, or (B.) move the loop to a region where more outward-pointing magnetic flux exists. Either one of these would induce a clockwise current to create inward pointing induced magnetic field within the area enclosed by the wire loop. The long straight wire creates a magnetic field that points out of the page above the wire and into the page below the wire, and our rectangular loop is below the wire, which means it's in a region where the external magnetic field (created by the long straight wire) is pointing inwardly. So, it looks like our best option is Choice (A.), because we can easily move the loop to a region where there's less inward-pointing magnetic flux by simply dragging the loop a little farther away from the long straight wire. If we instead moved the wire loop towards the long straight wire, it would be sending the loop to a region where more inward-pointing magnetic flux exists (because the long straight wire's -field is stronger there), which would cause the loop to try to induce some outward-pointing magnetic flux, but that can only be achieved by inducing a COUNTERCLOCKWISE current, and that's not what we want.

Real/ virtual images can be photographed.

Both

Real/virtual images can be created with converging lenses

Both

once the incident angle θ_1 ______ the critical angle, no light from the first medium will ever enter the second medium; it will all be _________ back

But once the incident angle θ_1 exceeds the critical angle, no light from the first medium will ever enter the second medium; it will all be reflected back

What to do if you want to induce an electric current without a battery

Change the magnetic flux Φ_B=B⋅A⋅cos⁡〖θ_BA 〗 through the circuit (either by changing B, or changing A, or changing the angle between them θ_BA) Only while the magnetic flux is changing will an induced current be created in the circuit But currents don't just flow for no reason They flow because a voltage must exist in the circuit to compel current to flow Today, we learn how to calculate that induced ΔV_Induced

these light rays do not look like they're converging anywhere you can't find a place in real space on the front side of the mirror where these light rays look like they're both headed they look like they're spreading out if they don't look like they're going to one location to meet up then instead it must look like they have diverged from somewhere behind the mirror. Concave or convex?

Convex

Convex mirrors only make ______, ________, _________ images.

Convex mirrors only make smaller, upright, virtual images.

**An electromagnetic wave travels out of the page (in the z-direction). Its electric and magnetic components are shown at a Single Instant in time (see figure) Could the following antennae orientations/types could receive this signal? Could the following antennae orientations/types could have produced this signal? y-axis rod antenna

Could not detect nor produce this signal If you want to detect (or produce) this wave, you'll have to be able to detect/create a wave whose electric component oscillates left and right. The only way to do that with a linear rod-shaped antenna is to have it horizontally-oriented so that when the oscillating (left/right) electric field component comes through, it will push the charges on the horizontal rod left and right, thus creating a left/right alternating current on the receiver antenna. The same could be said in reverse order for the broadcast antenna.

** When white light enters a new material, it may spread out into its constituent colors. This process is called _____________.

Dispersion

Define wavelength. Units? Symbol?

Distance from peak to peak on an EM wave (meters) λ (lambda) wavelength it might be tiny it could be you know nanometers it could be huge it could be a kilometer

Diverging Lenses We always take their focal length to be a positive/negative distance.

Diverging Lenses We always take their focal length to be a negative distance.

**Does the following scenario produce electromagnetic waves? A beam of neutrons accelerating in a straight line

Does NOT make EM waves Only accelerating charged particles create ripples/waves in the electric and magnetic fields. Those waves propagate outwards at the speed of light, which we perceive as light (though not always visible). Note: "Acceleration" doesn't always have to mean in a straight line; it just means that your velocity vector is changing (either magnitude or direction).

**Does the following scenario produce electromagnetic waves? A beam of protons traveling in a straight line at a constant speed

Converging lens us can only create real images. True or false

False

Diverging lenses can create both real and virtual images. True or false

False

Is the follow statement true for EM waves moving through a vacuum (e.g., empty space)? All EM waves have the same amplitude.

False

Is the follow statement true for EM waves moving through a vacuum (e.g., empty space)? All EM waves have the same frequency.

False

Is the follow statement true for EM waves moving through a vacuum (e.g., empty space)? All EM waves have the same wavelength.

False

Real images can be created with diverging lenses. True or false

False

The speed of light in a vacuum is c = 299 792 458 m/s. This is the speed that all electromagnetic waves move. The only way to increase this speed is to use a longer wavelength EM wave. True or false?

False

**True or false of electromagnetic waves? If we want to send a radio wave ("signal") from Earth to Mars, a higher frequency EM wave would reach Mars faster

False Higher frequency EM waves do not travel faster. They all travel at the same speed (in a vacuum), . Making larger just makes smaller.

**True or false of virtual images produced by lenses and mirrors? Virtual images can only be magnified smaller than the original object

False There's nothing that prevents virtual images from being magnified bigger.

Virtual images can never appear on the same side of a lens as the object. True or false

False They have to

A magnetic field pointing out of the screen moves away from a wire loop. a current flow through this loop as it exits the magnetic field. What explains the origin of the induced current that flows through this wire loop?

Faraday's Law can be stated in two equivalent ways that make the same predictions: The induced voltage around a loop is proportional to the rate at which the magnetic flux changes (ΔV_Induced=-(ΔΦ_B)/Δt) Circular electric fields are created by time-varying magnetic fields This is not a situation where the wire itself moves, so Motional EMF doesn't explain this. Instead, the strength of the magnetic field penetrating the loop changes with time (because the field moves away), which means that curling electric fields are spontaneously created that push charges around the wire loop.

Sometimes we didn't do anything with the wire we just changed the magnetic field strength or maybe we changed the direction you leave the wire completely still and do something with the magnetic field and that's still induced a current due to what?

Faraday's law

What does carbon dioxide's ability to absorb and re-emit infrared light have to do with human-caused climate change?

Greenhouse Effect §Light from the sun (especially visible) impacts earth. It breaches the atmosphere, because CO2 is transparent to visible light and doesn't get absorbed. §But as earth heats up, the ground emits infrared (as all room temperature objects do), and a blanket of CO2 receives that infrared, absorbs it, and re-emits it in all directions, including right back down at the ground. §This is a feedback loop that's good at keeping us warm from empty space, but can accidentally result in runaway heating.

If you find two or more rays ___________________, you've found the location of an image

If you find two or more rays converging at one location, you've found the location of an image

Any ray that approaches the lens parallel to the principal access refracts: In converging lenses? In diverging lenses?

In converging lenses refracts out through the back focus F In diverging lenses refracts out the back in line with the front focus F (focal length always negative)

In converging lenses, whenever you find two rays that converge at one location you have found the ___________ __________

In converging lenses, whenever you find two rays that converge at one location you have found the location of an image

the word ________ it means to create to compel a current to flow where there otherwise shouldn't be one.

Induce -How magnetism creates electricity. the and induction is this beautiful connection between electricity and magnetism that very nearly completes their story because up to now you have seen electricity create magnetism

What light spectrum is the band of frequencies immediately below red visible light (4×〖10〗^11 Hz to 4×〖10〗^14 Hz)?

Infrared Light

Just Info: Ultraviolet can be created due to molecular motion, but X-Rays and gamma rays are purely subatomic in nature, being emitted by atomic electrons and nuclei.

Just Info: •Due to their extremely small wavelengths, they tend to penetrate ordinary matter to tiny distance scales before being reflected or absorbed. •Gamma rays are produced in the most violent astrophysical events in nature.

A loop of wire moving right moves out of a magnetic field pointing into the screen. In which direction will a current flow through this loop as it exits the magnetic field?

Lenz's Law tells us the direction of the induced current when the magnetic flux changes through the area enclosed by a loop of wire. It's a process that goes like this: 1.Does the flux change? If so, how? Yes, the flux through the area enclosed by this wire loop disappears. 2.How will the loop of wire respond to this change? The wire will respond by opposing this loss of flux, which means it will have to make more. That means induce a magnetic field that points into the screen to compensate for what's lost. 3.In which direction would a current need to flow to create this response? To create more magnetic field that points into the screen, the wire must make a clockwise current according to RHR2. thumb into screen fingers to right

In the h i divided by h o equation, what does the minus sign mean?

Magnification equation the minus sign will be important because the magnification has to account for sometimes being upside down and negative mirrors

**Does the following scenario produce electromagnetic waves? A beam of electrons accelerating in a straight line

Makes EM waves Only accelerating charged particles create ripples/waves in the electric and magnetic fields. Those waves propagate outwards at the speed of light, which we perceive as light (though not always visible). Note: "Acceleration" doesn't always have to mean in a straight line; it just means that your velocity vector is changing (either magnitude or direction).

A diatomic molecule is exposed to a passing EM wave. Assuming the E-field is never strong enough to separate the bond between the ions, what will effect will this E-field have on the molecule?

Microwave Ovens §Polar molecules (with a +V and -V side) get twisted and rotated as microwave E-field oscillations move through. §Microwaves aren't energetic enough per wave to rip electrons off atomic nuclei ("ionization"), but they can cause friction between polar molecules through repeated rotation. §The water molecules in your food quite literally rotate/scrape against each other with Coulomb repulsion, which causes them to dissipate energy in the form of heat. §Since your plate/bowl has no water in it, it never gets hot from microwaves, except through conduction with the food it's touching.

A loop of wire moving right moves out of a magnetic field pointing into the screen. A current will flow through this loop as it exits the magnetic field. What explains the origin of the induced current that flows through this wire loop?

Motional EMF (short for "Electromotive Force" - an old-fashioned name for voltage) occurs when a wire is physically dragged in the presence of a magnetic field so that the flux through that wire loop changes. The free charges on the surface of the wire loop are thereby moving through a magnetic field and may experience Lorentz Forces that compel a current. Remember that this breaks no laws we've learned so far: the charges were already moving because the whole wire itself was moving, so they're vulnerable to magnetic forces.

sometimes we physically move a wire in and out of a magnetic field and that induces a current due to what?

Motional emf

Is this one of James Maxwell's predictions regarding electromagnetism? Freely moving magnetic charges act as sources of static magnetic fields

Would the following scenario would produce electric and magnetic fields whose strengths change with time? Electric charges moving at constant velocity

No Charges moving at constant velocity produce electric fields that move alongside them, but they make very static, boring, unchanging magnetic fields. Remember that moving charges make magnetic fields, but constant currents (a stream of constant velocity particles) make constant magnetic fields.

Would the following scenario would produce electric and magnetic fields whose strengths change with time? Stationary electric charges

No Charges that aren't moving produce electric fields, but they don't make any magnetic fields at all. Remember that moving charges make magnetic fields. If we're talking about making time-varying electric and magnetic fields, a stationary charge isn't good enough.

Define the frequency of a wave? Units? Symbol?

Number of waves passing per second on an EM wave (1/seconds = Hertz (Hz)) f or 'v' (Greek 'nu', not v) ex: it takes about three full seconds to go from one peak passing to the next so in terms of a frequency that would be one wave per three seconds or what we would call point three three hertz hertz just means per second one over seconds

total internal reflection

Occurs at critical incident angle a laser is shining inside water it's actually from the outside but the laser is clearly visible in the water and when it meets the boundary between water and air it never makes it out of the water it all bounces off it bounces off the boundary and goes right back into the water no amount of it escapes into the air that's total internal reflection total because none of it leaves internal because it all stays inside reflection because it bounces off so it's all reflected at the boundary between water and air this doesn't necessarily have to be water and air that's just an easy example to show

On the electromagnetic spectrum, higher energy is found on the {right/left} side of the spectrum with {higher/lower} frequency (pic)

On the electromagnetic spectrum, higher energy is found on the {left} side of the spectrum with {higher} frequency

Real/virtual images can be created with diverging lenses

Only virtual

In North America, power lines carry alternating current that oscillates 60 times per second, which creates EM waves in the radio frequency range. These ripples in the E and B fields have wavelengths of _______.

Radio waves §The speed of light, at which all EM waves move through space, is c=299 792 458 m/s, roughly 3×〖10〗^8 m/s. §If the charges in the wires oscillate at 60 Hz, then the wavelength of their EM waves is: λ=c/f=(299 792 458 m/s)/(60 1/s)≈5 000 000 m =▭(5 000 km)

**A ray of light travels from water to air, and then to diamond as seen at right. Which of the labeled rays shows the path taken by the light ray upon reaching the air-to-diamond boundary? (pic) a) Ray A b) Ray B c) Ray C d) Ray D e) Ray E f) Ray F g) Ray G

Ray C When the light enters a more refractive material (than both water and air), it should be refracted even more towards perpendicular than it was in either of the other two materials.

**A laser shines a light from water towards air as seen in the figure at right. The critical angle for this boundary is also shown. Which of the resultant rays (labeled A, B, C, D, and/or E) will be present in this scenario? (pic) a) Ray A only b) Ray B only c) Ray C only d) Ray D only e) Ray E only f) Some of the light will produce Ray D, and the rest will produce Ray E g) Some of the light will produce Ray B, and the rest will produce Ray E h)All of these rays will be present

Ray E only Beyond the critical incident angle, going from a more refractive material to a less refractive material, light will not make it out across the boundary. TIR dominates here.

A pencil sits in front of a concave mirror with incident and reflected rays traced from the pencil tip. In the previous question, if you were to look into the mirror, what kind of pencil image is seen by your eye?

Real This image is real because the two reflected light rays look like they're actually coming closer together to meet somewhere in real space. The location of their meeting will be the location that the image forms.

Real images form via [ Select ] ["refraction", "reflection"] on the [ Select ] ["opposite", "same"] side of lenses from where the light originates. Real images form via [ Select ] ["refraction", "reflection"] on the [ Select ] ["same", "opposite"] side of mirrors from where the light originates.

Real images form via [ Select ] ["refraction", ""] on the [ Select ] ["opposite", ""] side of lenses from where the light originates. Real images form via [ Select ] ["", "reflection"] on the [ Select ] ["same", ""] side of mirrors from where the light originates.

What colors probably moves at the fastest speed in window glass?

Red The index of refraction looks like n ≡ c v. Since red probably has the smallest refractive index in window glass of all the visible colors, that means n r e d = c v r e d must be a small number. The quotient n ≡ c v is smallest when v is largest. So red light must move at the fastest speed of all visible wavelengths while it's in window glass.

Rule: any ray that passes through the _____1______ gets reflected back out through the _____1_____ again

Rule: any ray that passes through the center of curvature gets reflected back out through the center of curvature again

The E -field component of the EM wave pushes free charges ______ along a ______receiving antenna via the Coulomb Force, F ⃗_E=q⋅E ⃗

The E -field component of the EM wave pushes free charges up/down along a vertical receiving antenna via the Coulomb Force, F ⃗_E=q⋅E ⃗ •The B ⃗-field component of the EM wave cannot cause free charges along a rod to start moving if they're not already. (Horizontal)

A bar magnet is held near a coil of wire connected to a light bulb. The magnetic flux Φ B = B ⋅ A ⋅ cos ⁡ θ B A through the coil of wire is changed. The area enclosed by the wire caused the change in magnetic flux during this event. Explain

The area vector A → has a magnitude (i.e., the size of the vector) equal to the area enclosed by the loop that's exposed to the magnetic field lines. Its direction always points perpendicularly outward from the face of the loop. The direction of the area vector didn't change, because the loop didn't face a different direction, so the angle between B → and A → didn't change. The strength of the magnetic field didn't change, because the field that is penetrating the area of the loop didn't become stronger or weaker. But the amount of area exposed to the magnetic field decreased. Since the size of A → changed and everything else stayed the same, the magnetic flux through the loop changed. This will cause the bulb to light during the event.

A pencil sits in front of a converging lens. What is the approximate focal length f of this lens? (pic)

The back focus at a position of 7 cm. The center of curvature of the lens is at a position of 5 cm. The focal length is the distance from the focus (either one if they're equidistant) to the center of curvature, f = 7 c m − 5 c m = 2 c m. The focal length of a converging lens is always a positive distance. Why? Because the Lens Equation makes good predictions if we treat it that way. That sounds like an unsatisfactory answer, but it's true.

A pencil sits in front of a diverging lens. What is the approximate focal length f of this lens?

The back focus at a position of 7.5 cm. The center of curvature of the lens is at a position of 5 cm. The focal length is the distance from the focus (either one if they're equidistant) to the center of curvature, f = 5 c m − 7.5 c m = − 2.5 c m. I wrote this subtraction in that order on purpose to remind you that the focal length is a negative number for a diverging lens, but no matter how I wrote it, this must always be true. Why does a diverging lens always carry a negative focal length? Because the predictions work out. ‍♂️

A bar magnet is moved closer to a coil of wire connected to a light bulb. The coil begins to receive more magnetic flux through the area it encloses. As this event occurs in real time, how will the coil of wire respond? Why?

The coil of wire will try to make less magnetic flux through its area to oppose this change Lenz's Law predicts the direction of the current that this wire will make in order to generate its own induced magnetic field to oppose any change in flux.

If the receiving antenna is a straight wire, which of the two components of the EM wave will produce a detectable signal in the receiver?

The electric or magnetic field component? •If the receiving antenna is a straight wire, which component of the EM wave will produce a detectable signal in the receiver? üOnly the E ⃗-field can cause the charges on the receiver antenna to start moving in this simulation. üThe E ⃗-field pushes with a Coulomb Force on the charges on the receiver to get them moving üRemember: magnetic fields can only push charges at right angles to where they're already moving, and they certainly can't cause charges to start moving if they're sitting still initially

The focal length is positive/negative (as always for a converging lens).

The focal length is positive (as always for a converging lens).

A pencil sits in front of a concave mirror with incident and reflected rays traced from the pencil tip. What is the approximate image distance d i in this scenario?

The image appears to form at a position of 4 cm. The mirror is at a position of 6 cm. The distance from the image to the mirror is d i = 6 c m − 4 c m = 2 c md i = 6 c m − 4 c m = 2 c m. It's a positive distance because it's not behind the mirror.

The image distance is negative, because the image is on the _______ side of the lens

The image distance is negative, because the image is on the virtual side of the lens

The magnification of the image is always given by: M≡h_i/h_o =(-2.3 cm)/(1.9 cm) = -1.2 -What is another way to calculate this? •What does the minus sign mean? •What does it mean that M>1?

The image is inverted •What does it mean that M>1? üThis means that the image is larger üWe also have another way of calculating it: M = -d_i/d_o = -(8.1 cm)/(6.5 cm) =-1.2 üThis is identical the ratio of the heights

**An object sits in front of a curved mirror as seen in the diagram at right. Several light rays are drawn from the object to the mirror. Use the table below to describe the IMAGE seen in the mirror. [NOTE: Assume that the light rays are drawn accurately.] (pic)

The image produced by this mirror is: a) Real b) Virtual a) Inverted b) Upright a) Smaller than the object b) Larger than the object

The induced voltage created in wire loop is called? Equation?

The induced voltage created in wire loop is traditionally called "E" ("E" for "Electromotive Force") But I'm going to call it ΔV_Induced to make it easier for you. The following is one of the ways to write Faraday's Law (but it applies to Motional EMF just as well): ΔV_Induced=-N(ΔΦ_B)/Δt

A bar magnet is held near a coil of wire connected to a light bulb. The magnetic flux Φ B = B ⋅ A ⋅ cos ⁡ θ B A through the coil of wire is changed. The strength of the magnetic field penetrating the wire coil caused the change in magnetic flux during this event. Explain

The magnetic field vectors B → get larger in size as you get closer to the bar magnet. The direction of the area vector didn't change, because the loop didn't face a different direction, and the direction of the magnetic field vectors didn't really change, because the bar magnet is facing the same direction, so the angle between B → and A → didn't change. The amount of area exposed to the magnetic field did not change. But the strength of the magnetic field penetrating the area enclosed by the loop of wire increased, because the bar magnet got closer to the wire loop. Since the size of B → changed and everything else stayed the same, the magnetic flux through the loop changed. This will cause the bulb to light during the event.

A bar magnet is held near a coil of wire connected to a light bulb. The magnetic flux Φ B = B ⋅ A ⋅ cos ⁡ θ B A through the coil of wire is changed. The angle between the magnetic field and area vectors caused the change in magnetic flux during this event. Explain

The magnetic field vectors B → point out of the north pole and into the south pole of the bar magnet. The amount of area exposed to the magnetic field did not change. The strength of the magnetic field didn't change, because the field that is penetrating the area of the loop didn't become stronger or weaker. The direction of the area vector didn't change, because the loop didn't face a different direction, but the direction of the magnetic field vectors didn't really change, because the bar magnet is facing the same direction, so the angle between B → and A → did change. Since the direction of B → changed (and therefore the angle between B → and A → changed), the magnetic flux through the loop changed. This will cause the bulb to light during the event.

What is the index of refraction? Symbol?

The measure of how much a ray of light bends when it enters a material. Symbol: n give us some sense of scale how much does stuff refract how much does light refract in a certain material this number will give us a score c as in charlie that's the speed of light in a vacuum v as in victor is the speed of light in a material whatever material it is could be air could be water could be glass plastic whatever it is light moves at a certain speed v in that material therefore that material has an index of refraction in which we can measure and when we measure it it helps us determine how much light slows down and bends when it encounters this new material. every single medium has its own index of refraction

question featuring the diverging lens, is the approximate object distance d o?

The object distance is the distance from the object to the center of curvature of the lens. The object is at a position of 0.5 cm. The center of curvature of the lens is at a position of 5 cm. The distance from the object to the mirror will be d o = 5 c m − 0.5 c m = 4.5 c m. This number is positive because the object is on the front side of the lens, but that's always where an object will be, because that's exactly what defines the front side of the lens (i.e., where the object is located).

**It is possible to form a real image at (or very near) the focal point of a concave mirror if: a) The object is moved extremely close to the mirror b) The object is moved within the focal length c) The object is moved beyond the focal length, but inside the center of curvature d) The object is moved beyond the center of curvature, but still close to the mirror e) The object is moved extremely far away from the mirror f) None of these

The object is moved extremely far away from the mirror (pic)

light ray is incident on the boundary between air and glass. What are the important angles?

The three most important angles for understanding this light's behavior are: θ 1, the "incident" angle at which the light impacts the boundary θ 1 ′, the "reflected" angle at which the light bounces off the boundary θ 2, the "refracted" angle at which the light crosses the boundary θ1 = 2 θ1' = 3 θ2 = 6

There is an uncountable number of applications to ___1_____, the ability to induce currents using magnetism without having a voltage source to propel them. But one application stands out among the rest for how it has changed the world: the electric generator.

There is an uncountable number of applications to electromagnetic induction, the ability to induce currents using magnetism without having a voltage source to propel them. But one application stands out among the rest for how it has changed the world: the electric generator.

What is true regarding the refracted angle θ 1 when TIR begins?

There is no single value of the incident angle θ 1 when TIR begins; it depends on the combination of materials through which light passes. Only Snell's Law of Refraction can tell us what the critical incident angle must be for any combination of materials.

"Alternating Current" is just current that rapidly oscillates back and forth in a wire. True or false

True

**True or false of virtual images produced by lenses and mirrors? Virtual images always exist on the "virtual" side of lenses and mirrors

True

**True or false of virtual images produced by lenses and mirrors? Virtual images are always produced by the appearance that light rays are diverging from somewhere else

True

**True or false of virtual images produced by lenses and mirrors? Virtual images are always upright and never inverted

True

**True or false of virtual images produced by lenses and mirrors? Virtual images can be photographed

True

**True or false of virtual images produced by lenses and mirrors? Virtual images cannot be projected onto screens

True

Converging lens can magnify images to M greater than one if object is within focal length. True or false

True

Converging lens can magnify images to M is less than one if the object is beyond focal length. True or false

True

Diverging lenses can never magnify images to M is greater than one. True or false

True

Diverging lenses can only magnify images to M is less than one. True or false

True

Is the follow statement true for EM waves moving through a vacuum (e.g., empty space)? All EM waves are ripples/oscillations in the electric and magnetic fields.

True

Is the follow statement true for EM waves moving through a vacuum (e.g., empty space)? All EM waves move at the same speed.

True

Is the follow statement true for EM waves moving through a vacuum (e.g., empty space)? If two EM waves have the same wavelength, they must also have the same frequency.

True

Real images are always on the real side of a lens. True or false

True

Real images can be projected onto screens. True or false

True

Real images can never appear on the same side of a lens as the object. True or false

True

True or false real images can be created with converging lenses

True

True or false. Real images are always inverted

True

True or false: mirror equation is the same as the lens equation?

True

Virtual images are always on the virtual side of a lens. True or false

True

Virtual images can never be projected onto screens. True or false

True

**True or false of electromagnetic waves? All EM waves move at the same wave speed in a vacuum

True Higher frequency EM waves do not travel faster. They all travel at the same speed (in a vacuum), . Making larger just makes smaller.

**True or false of electromagnetic waves? EM waves of different frequencies are perceived as having different "colors" (if they're visible to the human eye)

True Higher frequency EM waves do not travel faster. They all travel at the same speed (in a vacuum), . Making larger just makes smaller.

**True or false of electromagnetic waves? EM waves of different wavelengths are perceived as having different "colors" (if they're visible to the human eye)

True Higher frequency EM waves do not travel faster. They all travel at the same speed (in a vacuum), . Making larger just makes smaller.

**True or false of electromagnetic waves? The peaks of the electric and magnetic components of a traveling EM wave always point along perpendicular axes from each other

True Higher frequency EM waves do not travel faster. They all travel at the same speed (in a vacuum), . Making larger just makes smaller.

The speed of light in a vacuum is c = 299 792 458 m/s. This is the speed that all electromagnetic waves move. If c is a constant for all EM waves, then longer wavelengths mean smaller frequencies, and shorter wavelengths mean higher frequencies. True or false?

True Since c = λ ⋅ f is non-negotiable for EM waves, if λ goes up (becomes a longer wavelength), then f must go down (becomes a smaller frequency) to preserve the constant wave propagation speed, c.

Magnetic fields that vary with time create electric fields. Electric fields that vary with time create magnetic fields. True or false

True This is one of those great symmetries in nature, and it doesn't have to be "in a loop of wire." It is just universally true in all space.

magnification and thin lenses is exactly the same thing as what it would be in curved mirrors. True or false. Explain

True you have an object height you have an image height the relationship between them is always the ratio of the image height to the object height but of course due to geometry it also turns out that minus the ratio of the distances is equally valid you'll get the same answer either way so that is also unchanged from mirrors to lenses and also unchanged is that we treat inverted images as having negative height

time-varying Magnetic fields create time-varying electric fields True or false

True!!! (and vice versa)

time-varying electric fields create time-varying magnetic fields True or false

True!!! (and vice versa)

In the electromagnetic spectrum. Frequencies greater than visible light are?

Ultraviolet x-ray gamma

What is the underlying cause of induced currents during Motional EMF (where loops of wire are physically moved in or out of static magnetic fields)?

Unbalanced magnetic forces are ultimately responsible for inducing currents in Motional EMF scenarios

Assuming Total internal reflection (TIR) is possible across two materials with normal dispersion, which of the following colors of light is most likely to experience TIR first as you approach the critical incident angle?

Violet

What colors probably has the largest refractive index in window glass?

Violet

What colors probably bends the most at an air-to-glass boundary?

Violet This will also be the color that has the biggest index of refraction in glass.

**White light is incident on a water-to-air boundary. If the incident angle of this light is gradually increased, which individual color will totally internally reflect FIRST? Explain.

Violet Violet is usually the most refracted color of visible light (meaning, most bent towards perpendicular to the boundary) because it usually has the highest refractive index of all visible colors in dispersive media. That means it's also going to be the first color to not make it out of the first (more refractive) material and into the second (less refractive) material when total internal reflection (TIR) is starting to occur.

A medicine bottle sits in front of a flat mirror. Its image is shown on the right side (behind the mirror). What kind of image is seen by your eye?

Virtual In virtual images, the light rays do not converge to any one location in real space. Instead, if you trace back their line of sight, you'll see that they only appear to be diverging from a point behind the mirror - a place that they couldn't possibly have originated.

Real/virtual images are always upright.

Virtual Real are inverted

We always measure θ 1 and θ 2 angles relative to the _____

We always measure θ 1 and θ 2 angles relative to the normal line drawn at the boundary

In which of the following scenarios is Total internal reflection possible? When both materials are equally refractive. When the first material is more refractive than the second. When the first material is less refractive than the second. why?

When the first material is more refractive than the second. None of the other scenarios permit TIR, because they all cause the refracted angle to be less than or equal to the incident angle, when it needs to instead be greater. The answer to the next question will determine precisely how large θ 2 must be.

Is this one of James Maxwell's predictions regarding electromagnetism? A time-varying magnetic field induces electric fields

Yes

Is this one of James Maxwell's predictions regarding electromagnetism? Freely moving electric charges act as sources of static electric fields

Yes

Is this one of James Maxwell's predictions regarding electromagnetism? Magnetic field lines always form closed loops; they don't begin or end anywhere.

Yes

Is this one of James Maxwell's predictions regarding electromagnetism? Magnetic fields are created by moving electric charges and/or time-varying electric fields

Yes

Would the following scenario would produce electric and magnetic fields whose strengths change with time? Electric charges experiencing constant acceleration

Yes Accelerating electric charges is a great way to make E and B vary with time.

Would the following scenario would produce electric and magnetic fields whose strengths change with time? Rapidly oscillating electric charges

Yes Making charged particles rapidly bounce back and forth is a great way to make "time-varying electric and magnetic fields." The crazy thing is: once you make a magnetic field that varies with time (by bouncing back and forth), Maxwell predicted that that time-varying magnetic field then creates a time-varying electric field. What you wind up getting is E making B making E making B making E, and this propagates out away from the bouncing charge like a wave.

a change in magnetic flux in a circuit causes ________ where they shouldn't

a change in magnetic flux in a circuit causes currents to flow where they shouldn't they don't like it they don't like having their magnetic flux change and therefore they oppose it and they oppose it by fighting back and they fight back by trying to stop their magnetic flux from being changed and to do that they need to make a current move there's no battery there's no voltage source of any kind

a radio or a phone or whatever your electronic devices that communicates wirelessly and that information is interpreted it's __1____ that leaves one broadcast tower or antenna or something reaches your device the ____1___ interacts with your device and it's interpreted as sound or data or text or emojis or whatever it is that you do

a radio or a phone or whatever your electronic devices that communicates wirelessly and that information is interpreted it's **light that leaves one broadcast tower or antenna or something reaches your device the light interacts with your device and it's interpreted as sound or data or text or emojis or whatever it is that you do

**Which of the following optical devices can produce virtual images? I. Convex mirror II. Concave mirror III. Converging Lens IV. Diverging Lens

a) All of these Convex mirrors and Diverging lenses can only make virtual images and nothing else. The other two can make virtual images as long as you place the object within the focal length of each one.

a) Could detect & produce this signal If you want to detect (or produce) this wave, you'll have to be able to detect/create a wave whose electric component oscillates left and right. The only way to do that with a linear rod-shaped antenna is to have it horizontally-oriented so that when the oscillating (left/right) electric field component comes through, it will push the charges on the horizontal rod left and right, thus creating a left/right alternating current on the receiver antenna. The same could be said in reverse order for the broadcast antenna.

** Which of the following electromagnetic waves (with wavelengths shown) has the highest frequency? Explain. a) Gamma Rays (m) b) Infrared Light (m) c) Microwaves ( m) d) Radio ( m) e) X-rays ( m) f) Visible Light ( m) g) Ultraviolet Light ( m)

a) Gamma Rays (m) The highest frequency corresponds to the shortest wavelength.

**In which of the following materials would light travel at the SLOWEST speed? a) Ethanol (n=1.36) b) Liquid Helium (n=1.03) c) Silicon Carbide (n=2.65) d) Human Cornea (n=1.38) e) Acrylic (n=1.49) f) Germanium (atomic number 32)(n=4.05) g) Gaseous Helium (n=1.00) Light always travels at the same speed (c)

a) Germanium (atomic number 32) (n=4.05) Because the index of refraction is defined to be , the materials that have the largest value of must have the smallest value of (since it's in the denominator). So light would move fastest through the gaseous helium, and slowest through the germanium.

although these light rays can't actually go through the ____1___ they do bounce off in line with the _____1____if you trace their line of sight back to a region where they can't actually have come from you will see that they do all align with the ____1____just like they would have in the case of concave/convex mirror where they can actually go through the focus (pic)

although these light rays can't actually go through the focus they do bounce off in line with the focus if you trace their line of sight back to a region where they can't actually have come from you will see that they do all align with the focus just like they would have in the case of concave where they can actually go through the focus

let's say i have a bar magnet and i'm going to bring it farther from the loop of wire, if i bring it away from the loop of wire you will see the flux through that loop... ?

and it will still fight that take this bar magnet away the flux goes down it doesn't like that the loop hates the fact that you just changed its flux and so now it tries to make a magnetic field point the other way to try to recoup what it lost there is no other guide to its behavior except always maintain the status quo whatever status you have in magnetic flux do you have a lot you have a little do you have none it doesn't matter what you have it will try to maintain exactly that amount until you stop changing it and when you stop changing it it stops fighting you and it only induces this magnetic field while you are trying to change the flux through it it will be happy with any amount of magnetic flux as long as you don't try to change it once you've changed it it will then be happy with that amount but if you try to change it again it'll fight you until you stop changing it and then it will be happy with that amount

antenna has two main parts it's got ____1__ and these stick out into the air and it also has a ______2 ______ and the ___2____ is supposed to provide an alternating ____2____so that you can get an alternating current on the ___1____

antenna has two main parts it's got nodes and these stick out into the air and it also has a voltage source and the voltage source is supposed to provide an alternating voltage so that you can get an alternating current on the nodes the voltage source is basically going to push charges back and forth or up and down voltage on these nodes oscillate so you'll see the voltage switch signs back and forth and as that happens these charges get pushed in opposite directions back and forth

Rule: any light ray that approaches this concave mirror parallel to the principal axis reflects out through the ________

any light ray that approaches this concave mirror parallel to the principal axis reflects out through the focus

any light ray that comes in _____1______to the principal axis goes out through the focus in a concave mirror it doesn't matter whether it came from the tip of the pencil the eraser the middle of the pencil makes no difference wherever you draw a light ray coming from this pencil if it's _____1______ to the principal axis as it approaches the mirror it's going out through the focus

any light ray that comes in parallel to the principal axis goes out through the focus in a concave mirror it doesn't matter whether it came from the tip of the pencil the eraser the middle of the pencil makes no difference wherever you draw a light ray coming from this pencil if it's parallel to the principal axis as it approaches the mirror it's going out through the focus

because the image shows up behind the mirror or that's what it looks like we're going to have to call the image distance a ________ distance to keep consistent with the mirror equation

because the image shows up behind the mirror or that's what it looks like we're going to have to call the image distance a negative distance to keep consistent with the mirror equation

bent closer towards the normal line that's how you can tell that you have entered a material that slows/speeds light down/up more than what it was in first material

bent closer towards the normal line that's how you can tell that you have entered a material that slows light down more than what it was in first

how to generate radio waves?

by accelerating electric charges back and forth on an antenna

call the critical incident angle theta c it's an incident angle it's the angle that you aim the light but it's special it's not just any angle it's the one that causes _______ to start

call the critical incident angle theta c it's an incident angle it's the angle that you aim the light but it's special it's not just any angle it's the one that causes total internal reflection to start

What is the front side of a converging lens? Back side? Also called? How to draw? Explain. How are they unlike mirrors?

called the front side and that's anything on the side of the lens from which the light originated it originated on that side and we also call that the virtual side because light doesn't actually refract there in fact it hasn't even gotten to the lens yet if it's on the front side once it goes through the lens and refracts twice once going in and once going out we call that the back side once it exits the lens that's the real side we call it the real side because the light has actually refracted on its way out of the lens so these two parts the front side and the back side characterize the regions around the lens and you may hear me call them virtual side and real side as well that's a clue as to what kind of images form on each one of those respective sides so converging lenses have a center of curvature at the center of the lens that's in here now having talked about what exists on the real side and on the virtual side i want to alert you the converging lenses unlike mirrors don't just have a single focus there's a focus on the real side and a focus on the virtual side and the reason for that is pretty simple light could come from one side go through the lens refract and come out the other side but it could also go the other way it's a lens it has two sides so there are two foci not just one single focus simply because light could come from either direction now if the lens is symmetric the foci will be equidistant from the lens and ours always will be i'm never going to give you a situation where the foci are not equidistant now we should talk about ray tracing one of the most important things you can do with lenses just like mirrors the goal is always to predict the location size and orientation of the image that you would see if you looked through the lens and also just like mirrors it comes from tracing several rays i'm going to draw two rays that emanate from one part of this object in this case it's a pencil and i'm going to choose the place from which the rays originate as the tip of the pencil as always just like with mirrors if you trace rays that emanate from the tip of the pencil if you form an image with those rays they will once again show you the tip of the pencil in the image the first ray that i'm going to draw is going to go toward the lens parallel to the principal axis and when it leaves it refracts out through the back focus when i say the back focus i mean the back side not the front side of the lens where the object is but the back side where the light has exited the lens any ray that approaches the lens parallel to principal axis will refract and it will exit going out the back focus now the next ray that i draw for a converging lens will be one that passes through the center of curvature and it's the only ray that remains mostly unchanged and i have to put an asterisk by this word mostly because i'm going to draw it as if that ray does not refract at all

Which can make real images? virtual images? concave/convex mirrors converging/diverging lenses

concave mirrors and converging lenses can make both real and virtual images, but convex mirrors and diverging lenses can only make virtual images.

Concave mirror uses and examples

concave mirrors are caved in you might use them as a cosmetic mirror you might use them to magnify stuff you might even use them to focus light in the bottom left picture you can actually see somebody focusing light rays on a leaf to catch it on fire please use concave mirrors responsibly if you have a cosmetic mirror and it magnifies i guarantee you it is a concave mirror it's caved inward if you look at it from the side it looks kind of like a c shape or a backwards c

concave mirrors are spherical which means that if you continued their shape they would make a sphere and every sphere has a center and so does a concave spherical mirror it has a center a __________. symbol is ____

we still want to draw a ray that comes in parallel to the principal axis only this time it can't reflect out through the focus instead it reflects out in line with the focus once again you -- concave or convex mirror?

convex

convex mirrors are used in?

convex mirrors are used in stores for security purposes they're used to help you peek around corners if you're wondering in the top right corner that picture was taken in the modular village near garage 2 and the person taking the picture is me that mirror is there so people don't walk around the corner and get hit by a golf cart. on the passenger side the mirror is always convex

__________ means that the wavelength causes you to have different indices of refraction. if you get a different refractive index for a different wavelength then it means it bends at a different __2__ for a different wavelength and if it bends at a different __2__ for a different wavelength then maybe that affects when total internal reflection begins as well

dispersion means that the wavelength causes you to have different indices of refraction. if you get a different refractive index for a different wavelength then it means it bends at a different angle for a different wavelength and if it bends at a different angle for a different wavelength then maybe that affects when total internal reflection begins as well

the images appear to be slightly smaller and upright in _________

diverging lenses

Examples of diverging lenses? What happens to light rays?

diverging lenses are actually the most common lenses used in corrective glasses because many people are nearsighted and nearsighted people tend to use diverging lenses you can see on the far left picture what a diverging lens effectively does to light rays it spreads them out what kind of image you might see

Explain James Clark Maxwell equations

e and b and q epsilon zero mu zero relationships between electric and magnetic fields between electric charges currents and magnetic fields 1. electric field lines flow out of and into electric charges that's what one of maxwell's equations says in symbols 2. magnetic field lines don't have any sources there's no such thing as magnetic charges you don't have magnetic fields emanating out of one thing and terminating into something else everything is a dipole they only make continuous loops these magnetic field lines 3. faraday's law very topical we just discussed it recently changes in magnetic flux induce electric fields you can also say time varying magnetic fields create electric fields 4. ampere's law sometimes called the ampere maxwell law steady currents create magnetic fields around the wires or also by symmetry time varying electric fields create their own magnetic fields it's numbers three and four that are going to be so crucial

electric charges make their own _________. When the charge is accelerated.

electric charges make their own electric field accelerated (pushed or pulled or sped up or slowed down in any direction) what you find is ripples you get electric and magnetic fields that vary with time and they make these outward moving ripples these bubbles almost when you accelerate electric charges and only accelerating electric charges can create a **time varying e or b field but once you start that process this ripple will expand outwards forever that ripple in the electric field **Only accelerating charges create time-varying E/B fields**

Explain alternating current on Antennae

electric field in and around this antenna as this charge gets shifted up and down the nodes so the first thing you'll notice is that as the current starts to switch you find that this charge has now made its way partially down the top node now in doing so it's starting to become intermingled between negative charges where there was a lot of positive charge at the top and probably a huge negative charge at the bottom due to their absence as they start to come back towards the center they kind of mix a little bit and they make weaker electric fields because they become co-mingled what you'll notice also is that the original electric field vectors that we saw on the previous slide are still present only now they have migrated slightly outwards you can still see them but they've now moved out on either side of the charge so let's let this process keep going and now it has passed the halfway point and its electric field vector in this region is starting to point up even though the charge has not fully moved all the way to the bottom yet and we can keep this going further and you can see the pattern is we've started to develop a wave the wave moves outward in all directions and the electric field is being whipped up and down you can see places where there is a really strong electric field pointing down and then it gradually becomes no electric field and then it starts to point up and it becomes strong and there becomes no electric field and then it starts to point down and becomes strong all of this whip-like motion in the electric field expands outward just like that ripple the bubble that you saw (can go right and left not just up/down)

electricity create ___1_____where you have moving electric charges individually or as part of a current they create their own ____2____ as they move like in the image that you see on the screen we have a coil of wire and we have some iron filings located around it when we turn current on in the wire the moving charges in the current make a ____2______ and you can actually see it in the iron filings

electricity create **magnetism where you have moving electric charges individually or as part of a current they create their own ***magnetic fields as they move like in the image that you see on the screen we have a coil of wire and we have some iron filings located around it when we turn current on in the wire the moving charges in the current make a **magnetic field and you can actually see it in the iron filings

electromagnetic waves have ___1___, ___2__, and ___3____ but instead of different _____2____producing different pitches like sound waves different ____2___ of electromagnetic waves produce different kinds of light if the light is visible these _____2____will correspond to different colors

electromagnetic waves have amplitudes wavelengths and frequencies but instead of different frequencies producing different pitches like sound waves different frequencies of electromagnetic waves produce different kinds of light if the light is visible these frequencies will correspond to different colors

Reflection at the boundary of light when it reaches another medium. Explain normal line.

every single angle that i reference in the context of reflection and refraction will be measured against a dotted line that i'm calling the normal line normal meaning perpendicular perpendicular to what perpendicular to the boundary between two materials anytime you have two materials or light is encountering that boundary at whatever location the light actually impacts the boundary you can draw a little dotted line perpendicular to that spot perpendicular to that boundary where the light impacts and all of the angles that i mentioned today will be measured against the light ray and that normal line

f is always positive/negative for converging lenses

f is always positive for converging lenses

The speed of light in a vacuum is c = 299 792 458 m/s. This is the speed that all electromagnetic waves move. The only way to increase this speed is to use a higher frequency EM wave. True/false?

false

let's say i have a bar magnet and i'm going to bring it closer to the loop of wire if i bring it closer to the loop of wire you will see the flux through that loop increase/decrease? What will the loop creates to oppose that change?

flux through that loop increase it'll get bigger and watch what happens in response the flux gets bigger and you'll see the magnetic field that points the other way that the loop creates to oppose that change

focal length is on the back side of the mirror we treat it as a ________ distance it's like in mirror land it's on the opposite side of the mirror

focal length is on the back side of the mirror we treat it as a negative distance it's like in mirror land it's on the opposite side of the mirror

_________in an EM wave is understood as color. the higher the frequency, the more ______________ it will appear.

frequency in an EM wave is understood as color. the higher the frequency, the more blue/violet it will appear. --there's an infinite number of different frequencies that light could have and all we can see is the visible part

_________in an EM wave is understood as color. the lower the frequency, the more ______________ it will appear.

frequency in an EM wave is understood as color. the lower the frequency, the more redder it will appear. --there's an infinite number of different frequencies that light could have and all we can see is the visible part

glass has a refractive index of about ____ water has a refractive index of about ____ air has a refractive index of about _____

glass has a refractive index of about 1.5 water has a refractive index of about 1.3 air has a refractive index of about 1.003

define magnification. Explain how to calculate and possible answers

h i divided by h o magnification the way we defined it is just the relative height of the image compared to the original object if the original object was a height h o height of object and the height of the image is h i the height of image then the ratio of those two the image height divided by the original object height is how we define magnification if the image had been huge then the magnification would be a number much bigger than one in our case it kind of looks like the image is going to appear upside down and slightly smaller and so we would call that a negative height because it's below the principal axis and a number that's less than one because the image height is smaller than the original object so the magnification here might be say minus 0.5 if the image is only half as big as the original object and upside down if you had an image that was twice as big and right side up it might have a magnification of plus two one other really interesting fact solely due to geometry

A pencil sits in front of a converging lens with incident and refracted rays shown. What is the approximate image distance d i in this scenario? (pic)

he image distance is the distance from the image location to the center of curvature of the lens. Because the image appears in front of the lens (on the "virtual" side), it will have a negative image distance, just like we saw for virtual images with mirrors. The image is located at about 3 cm. The center of the lens is located at 5 cm. The image distance will be d i = 3 c m − 5 c m = − 2 c m. If you check this against the values of d o and f, you will indeed find that the image distance is a negative number. 1 d o + 1 d i = 1 f → 1 1 c m + 1 d i = 1 2 c m → d i = − 2 c m

How much converging lenses refract depends on?

how thick the lens is and of course what the lens is made of if it's made of glass then you'll need to know the index of refraction for glass

should i draw the object distance as from the object to the edge of the lens or to the center of the lens

i base everything on the center of the lens because the lens is assumed to be very thin

if it encounters a material that's slower/faster or that causes it to move faster/slower it will be less/more refracted in other words bent closer towards/further away from that normal line

if it encounters a material that's slower or that causes it to move slower it will be more refracted in other words bent closer towards that normal line

bent further from the normal line that's how you can tell that you have entered a material that slows/speeds light down/up more than what it was in first material

if it entered a material that slowed it down less that allowed it to go faster that light ray would be bent less towards the normal line

if it's a convex mirror where the focus and the center of curvature are behind the mirror the ________________ would be called a negative number

if it's a convex mirror where the focus and the center of curvature are behind the mirror the focal length would be called a negative number

if the magnetic flux through a loop of wire changes from whatever it is right now, the wire will do what? Why?

if the magnetic flux through a loop of wire changes from whatever it is right now it doesn't matter how much it is if it at all differs from one moment to the next then the loop gets angry the wire loop gets angry and it fights back by creating its own induced magnetic field to try to oppose the way that you just changed its flux but again only while the flux is changing once you stop changing it it becomes happy with its new status quo

if the tip of the pencil was previously above the principal axis and now you find it below the principal axis in the image that you see in the mirror it might be an ____1____ image you may also surmise that it doesn't appear that this image where the pencil tip appears to be is going to be quite as tall as the original object so maybe it's ________2____

if the tip of the pencil was previously above the principal axis and now you find it below the principal axis in the image that you see in the mirror it might be an inverted image you may also surmise that it doesn't appear that this image where the pencil tip appears to be is going to be quite as tall as the original object so maybe it's magnified

if you can figure out which way the current's going to flow you know exactly which way the what is pointing? Explain.

if you can figure out which way the current's going to flow you know exactly which way the electrodynamic field is pointing because they're the reason that the current moves in the first place they're responsible for pushing those charges into motion so the direction of an electric field that's created by a time varying magnetic field is not too hard to figure out once you understand which way the current was moving because they're the ones that pushed it into motion in the first place faraday's law of induction

Explain focus? location? importance? symbol?

if you have light rays that approach the mirror parallel to that principal axis they all get reflected out through the same point no matter where they go they all wind up crossing the same point and that point is called the focus we label it f in fact if the center of curvature is one radius of curvature away from the mirror the focus in a spherical concave mirror is always half of that it's half of one radius so it's a quarter of the diameter of the whole sphere

if you know where the _____ ____ is for this lens all of the distances can be based on that

if you know where the center of curvature is for this lens all of the distances can be based on that

Reflection at the boundary of light when it reaches another medium. Explain angle of incidence.

incidence that means the angle that the light is incident on the boundary the incoming angle is exactly the same as the outgoing angle the angle of reflection in fact if you compare the two angles which we call theta one the incident angle and theta one prime with the little apostrophe theta 1 prime the reflected angle those two angles are always the same the reason i say this is one of the simplest physical laws you'll ever see is because all it says is two things are equal the angle that you come in is the angle you go out it's easiest to imagine a mirror in the case of a mirror almost all the light is reflected at the boundary very little of it actually enters the glass and if it does it hits a super reflective surface right behind the glass

Describe Lenz's Law

induced current flows in a direction that opposes the action that induced it. - that a loop of wire makes its own magnetic field we call it an induced magnetic field and it does this to oppose any change in magnetic flux that it experiences it's almost like the loop of wire has a mind of its own it's almost like the luba wire is a petulant child that does not want you to change its magnetic flux and it will do anything necessary to keep that the same. if the flux through the loop of wire changes the wire loop makes its own new magnetic field specifically to oppose the change that you made to its current situation now this is a perpetual game of opposites

§We've now completed the journey through the frequencies of the EM spectrum up to and including visible light. §From now on, all light with frequencies higher than 8×〖10〗^14 Hz will be ________ EM radiation, because it carries enough energy per wave to strip individual electrons away from their atomic nuclei.

ionizing §The only danger from lower frequency EM waves is generally due to molecular heating (e.g., microwave ovens). §But these next three bands cause cancer in humans in high doses with repeated exposure.

How does a wave travel?

it does travel in a straight line but it does so in all directions expanding outward like a sphere it's just really hard to illustrate that it's much easier for us to illustrate it moving along one little line as if it's attached to a string but in reality it moves outwards in all directions because if you think about it if you happen to be on one side of town and you're trying to get cell phone service you would really hope that that magnetic and electric oscillation would happen in all directions

The wire will _____________ to fight any change to the flux that you try to make. How?

it will induce its own magnetic field to fight any change to the flux that you try to make -how does a simple wire loop even make its own magnetic field anyway you want to make a magnetic field that points in this direction it's the same way that anything makes a magnetic field you need moving charges moving charges make their own magnetic fields now let's suppose that this loop of wire induces its own magnetic field that points down inside the loop once you know that the magnetic field that is induced by this loop of wire will point down -you can use the ***second right hand rule*** to figure out which way the current must have gone because it's only a current that can make this purple magnetic field you have to work backwards by knowing which direction the induced field points because you know which way it wants to fight back and from that information you backtrack to figure out which way the current must have gone and the second right hand rule you recall is very flexible because it allows you to use your fingers as the current and you don't know the current yet right but that's the whole point we're going to figure out which way the current must have gone by pointing our thumb towards where we know the induced field must be if i already know the induced field must point down then i point my thumb down and the only way that my fingers can bend around this loop of wire is what appears to be clockwise from above only a current that looks like this would create that magnetic field inside the loop of wire so the wire obtains this induced current it uses that induced current to create an induced magnetic field and it uses that induced magnetic field to oppose the change in magnetic flux that you tried to give it but in principle we have to work backwards to figure out which way that red current must have been we started with number three we then went to number two and then we can understand number one only through the second right-hand rule so we understand that magnetic flux changes through loops of wire and when it does the wire fights back it fights back by making its own magnetic field to oppose that change how does it make a magnetic field it needs a current which weight is the current point the second right hand rule can show us

What is a real image?

it's an image that appears in a location where light rays converge to a single spot what you just saw is light rays impacting a curved mirror bouncing off and converging in real space in some location you can see the spot that they all converge where those light rays meet real light rays actually went there and they all converged on that location before continuing on their journey

Area vector in Magnetic flux points in what direction? most magnetic flux when?

it's part of calculation that goes into this strength of the magnetic flux because we need to know how much area is exposed to magnetic field lines that are trying to penetrate it so the magnitude of this area vector the size of that that blue vector how big is it its magnitude is equal to how much area there is and its direction is always perpendicular to the direction the loop of wire faces straight out from the face and magnetic field lines may penetrate this loop of wire depending on what angle they're aimed but of course remember that there isn't actually area in the sense that it's not a metal surface you're not looking at a metal tray this is just a loop of wire -the area vector of the loop if there is an angle you'll be able to see it when the vectors are placed tail to tail you'll notice that the magnetic flux depends on the cosine of that angle cosine measures overlap it measures how much two vectors point in the same direction so cosine is biggest when b and a point in the same direction that means you get the most magnetic flux -almost like air moving straight through an open window when the magnetic field lines are oriented 90 degrees relative to that area vector cosine of 90 degrees is zero and that makes sense as well because that's a situation where the magnetic field lines don't penetrate the area at all and instead run directly past the loop

What is Faraday's Law? Ampere's Law?

just empty space and the only thing that exists there are the fields according to **faraday's law if you have a magnetic field (B) that changes with time it creates its own electric field (E) and according to **ampere's law if you have an electric field that varies with time it creates its own magnetic field (B) notice that i said nothing about electric charges i just said if these fields do this then they create each other so this shows symmetry between electricity and magnetism

all electromagnetic radiation moves at the speed of _____

light 300,000,000 m/s in a vacuum

light only travels at its maximum speed when it's in a ________ that's also the maximum speed that anything in the universe can travel any other time if light is in some other medium anything especially anything made of atoms it's going to go slower than its maximum speed

light only travels at its maximum speed when it's in a vacuum that's also the maximum speed that anything in the universe can travel any other time if light is in some other medium anything especially anything made of atoms it's going to go slower than its maximum speed

________ as well as useful tools to help visualize how electric charges push and pull on each other at a distance we said they make these fields and it's the fields that do the pushing and the pulling

magnetic fields as well as useful tools to help visualize how electric charges push and pull on each other at a distance we said they make these fields and it's the fields that do the pushing and the pulling. fields are real they are their own thing they can create each other whether you have electric charges doing something or not the fields can dynamically create each other like twins they are their own thing they're not just a helpful visualization technique the fields are real they are physical they are part of the real

What is magnetic flux? Symbol? Units? measures?

magnetic flux has the symbol phi (ϕ) phi with the subscript b -It measures how well external magnetic field vectors penetrate the area enclosed by a loop of wire (like airflow through an open window - airflow with magnetic flux, wind with magnetic field lines, and a window with a loop of wire) -units of tesla times meters squared

magnetic flux is a measure of? What affects it?

magnetic flux is a measure of how well magnetic field lines penetrate an area enclosed by a loop of wire it's got three things that go into it how strong is the magnetic field that's penetrating that area how big is the area and what is the cosine of the angle between b and a remember that a point straight out from the face of the area enclosed by the loop of wire and cosine measures overlap so when b and a point in the same direction you have a lot of magnetic flux if you like my airflow analogy you have a lot of airflow

Coil of wire connected to a light bulb. To make the bulb light up what you won't find is a battery, if this bulb lights up it is solely because of what you're doing there is no battery no voltage source. what you find is that the bulb only lights up when? Why? What is this called?

magnetic flux is changing only while it's changing does a current flow through this circuit. if you change the magnetic flux through that coil you created a current where there should not be one now the way we explain this phenomenon is called **Lenz's law**

How can magnetism can create electricity? Example.

magnetism can create electricity like changing the magnetic flux through a loop of wire induces a current if you notice in this animation you'll see somebody places a magnet inside a coil of wire and when they place it in or take it out you can actually see the little ammeter needle move and it moves in two different directions one direction the ammeter needle moves to the left the next time it moves to the right but notice that the ammeter is measuring a current in a coil of wire with no battery just from changing the magnetic flux through the coil with a bar magnet

What equation relates object distance, image distance, and focal length?

mirror equation d o the object distance from the object to the mirror the i the image distance the distance from the image to the mirror and the focal length f if you know two out of the three of these pieces of information you can always algebraically solve for the third one the mirror equation connects all three of these pieces of information as follows

Typically, more/less dense materials tend to slow light down more as it moves through them.

more Vacuum =1 Diamond=2.42 Window Glass= 1.52 Air = 1.0003 Water = 1.33

if you want to make more magnetic flux to make up for what you lost you'll have to make a clockwise current but it only begins when the flux starts to change and it ends when the flux stops changing that was due to what? Magnetic field points into screen

motional emf only exist when charges are already moving magnetic fields can't push charges that aren't moving to begin with so motional emf is really only good at explaining currents that we see when we ourselves are moving the wire loop by just physically dragging it somewhere

motional emf and faraday's law both of these represent the how and why of our discussion of _________ where currents electric currents are induced or they otherwise shouldn't exist

motional emf and faraday's law both of these represent the how and why of our discussion of electromagnetic induction where currents electric currents are induced or they otherwise shouldn't exist

What is Snell's Law? equation? what does it give you?

n1sinθ1 = n2sinθ2 The refracted or incident angle n1 being the index of a fraction of the first material the incident material the one that the light is trying to leave n2 being the refractive index of the second material the one that it's trying to get into

When light leaves a more refractive medium and enters a less refractive medium, does the light bend more or less towards the normal line at the boundary?

n2<n1 Less refracted •When light leaves a more refractive medium and enters a less refractive medium, does the light bend towards normal? •The light bends less (toward normal) in less refractive media. •This means that n_1>n_2. •You can see that θ_2 is clearly bigger than θ_1 because the refracted ray is bent less toward the normal line.

The index of refraction for empty space (vacuum) is:

n=1

The index of refraction for window glass is:

n>1

nature apparently doesn't like it when magnetic flux changes and it and it induces a ___1____ to try to fight back the direction of that ___1_____ is determined by ________2_______

nature apparently doesn't like it when magnetic flux changes and it and it induces a current to try to fight back the direction of that current is determined by lenz's law

nature doesn't like changes in magnetic flux we just said that it's unhappy about it, what are the two different reasons for why currents get induced?

nature doesn't like changes in magnetic flux we just said that it's unhappy about it well we've now seen two different reasons for why currents get induced one is motional emf where lorentz forces cause currents to start moving but that's because the wire itself was already being moved through a magnetic field or into one or out of one and the second way this happens is faraday's law and this doesn't have anything to do with the wire moving this is time changing magnetic fields magnetic fields that change some way with time either they get stronger or weaker or they change their direction or something that magnetic field that changes with time creates its own electric field that bulldozes charges around a wire loop and the most amazing part about it all is that whether there's a wire loop there or not those electrodynamic fields are getting made they are real when a magnetic field changes with time it makes its own time varying electric fields too and the electric fields curve they make concentric rings they make continuous loops if you happen to have a wire loop sitting there it'll compel charges to start moving around as a current but the fields do this all on their own they don't care whether there's a wire loop there or not they will do this no matter what now in either case whether it's motional emf or faraday's law the rate that the magnetic flux changes causes basically an effective voltage you get an emf you get basically a voltage source a charge pusher and it basically acts like a battery

Will the bulb connected to conducting wires glow? (The wires plus bulb system is aligned with the z-axis.)

now in either case whether it's motional emf or faraday's law the rate that the magnetic flux changes causes basically an effective voltage you get an emf you get basically a voltage source a charge pusher and it basically acts like a battery and i'm now ready to show you quantitatively what that looks like the induced voltage that you get that acts just like a battery briefly depends on the rate at which the flux changes the bigger the rate of change of magnetic flux the bigger the voltage you can induce again no actual battery is necessary to do any of this you just have to change the magnetic flux to the coil of wire and if you do it you get a current and the current happens because of this voltage and the voltage happens because the flux changed

often associated with temperature and "thermal" imaging cameras because room temperature objects tend to emit ________ light all the time - they glow.

often associated with temperature and "thermal" imaging cameras because room temperature objects tend to emit infrared light all the time - they glow.

once i reach that __________ all refraction has disappeared if i'm below it refraction happens as normal if i meet that one angle all the light ________

once i reach that incident angle all refraction has disappeared if i'm below it refraction happens as normal if i meet that one angle all the light totally internally reflects off the boundary and it never makes it inside the second material in this case the second material is probably air it doesn't go into the air it just bounces off and comes right back

where won't you see light refract at the boundary?

one is if the light is incident at an angle of zero degrees which means it comes perpendicularly straight into the boundary like head first into the boundary so then it it passes through into the second material it just doesn't noticeably bend because it came in perpendicular anyway but then the other really weird case is where it all gets reflected at the boundary and it never crosses over it now that's a special case we'll see in the next lecture not lecture 21 but in lecture 22 we will encounter a situation where light does come in at an angle to a boundary but none of it refracts that's a very rare situation we will see that next time

Unlike converging lenses, diverging lenses? converge light? real side?

one they never converge light to a single point on the real side of the lens they only diverge it out the back side you can check that with snell's law of refraction if you're not sure watch the rays come in draw the normal line at the boundary and do another one when they exit and you will find that these lenses necessarily spread light out that has a consequence for the kinds of images that they form they may bear quite a bit of resemblance to convex mirrors

What is the direction of the magnetic field created by the long current-carrying wire? Vertical wire with current flowing up If loop moving away to regions of weaker external magnetic field, what happens with magnetic flux?

out of screen left side of wire into screen right side of wire 2RHR The magnetic flux through their enclosed area is reduced as they move away. üLoop lose magnetic flux. üTo oppose this change, it will try to create more magnetic flux to compensate. üTo create more magnetic flux through Loop B, it must create its own B ⃗_induced pointing out of the screen.

It's an imaginary dotted line that's always ______________ to the boundary between two media. It helps us visually identify relevant angles during reflection and refraction.

perpendicular

Draw/Interpret ray diagrams for concave and convex mirrors

pic

What is the lens equation? What are the symbols mean?

pic

Where should we place an object on the real side of a concave mirror to produce a virtual image?

pic

_______ some people call it a _____________ that's just a horizontal line that runs straight through the center of curvature

principal axis some people call it a primary axis that's just a horizontal line that runs straight through the center of curvature

radio microwave infrared visible ultraviolet x-rays gamma rays they were all just oscillations in the electric and magnetic field but they happen to oscillate at different _______they happen to have different _________

radio microwave infrared visible ultraviolet x-rays gamma rays they were all just oscillations in the electric and magnetic field but they happen to oscillate at different frequencies they happen to have different wavelengths

Explain the two things that can happen to light when it reaches another medium?

reflection/refraction

theta 2 is the name of what angle?

refracted angle incident angle is the angle that you aim it then you can tell me the angle that it comes out. theta 2 is pretty much always going to be the name of the refracted angle

Rule: if you find two or more light rays that appear to converge at one location then you have found the location of the _______ right here

rule if you find two or more light rays that appear to converge at one location it looks like they meet somewhere in space then you have found the location of the image right here you will see that two light rays converge at that location now of course they keep going after that but they do meet and if they cross paths an image will appear there if you were to look in the mirror you would see an image that looked as if it were at that location because they both left from the tip of the pencil where the red dot is found they are carrying information those light rays about the tip of the pencil so where they reconvene you will see the tip of the pencil there

In words, the function sin^ − 1 ⁡ ( x ) can be interpreted as:

sin − 1 ⁡ ( x )sin − 1 ⁡ ( x ) returns "θθ," the angle whose sine is xx. In other words, x = sin ⁡ ( θ )x = sin ⁡ ( θ ). The inverse sine function returns an angle, and if you take the sine of this angle, you'll get whatever you plugged into the argument of the inverse sine function. For example, sin − 1 ⁡ ( 1 ) = 90 o, because 90º is "the angle whose sine is" 1. Similarly, sin − 1 ⁡ ( 0.5 ) = 30 o, because 30º is "the angle whose sine is" 0.5. Finally, sin − 1 ⁡ ( 0 ) = 0 o, because 0º is "the angle whose sine is" 0.

The index of refraction for any medium is defined as n ≡ c v, where c is the speed of light in a vacuum and v is the speed of light in that medium. Generally, the greater the refractive index, the faster/slower light moves through that particular medium

slower

converging lenses examples?

some glasses feature converging lenses cameras other lenses even microscopes telescopes many different applications of converging lenses exist

the bigger the EM wave, the _____________ light

the bigger the EM wave, the brighter/more intense light ---if you hear intensity or you hear brightness you should think of them interchangeably and intensity is related to the maximum value of the e field as it propagates what i'm really saying is amplitude so in other words if you have a bigger em wave amplitude you are effectively getting brighter light if the electric field and the magnetic field deviate really far from their average value as the wave moves through that's a really intense em wave that's a really bright light but again i must say it doesn't always have to be visible light

normally dispersion happens where longer/shorter wavelengths which is the redder side of visible light carry smaller/larger refractive indices and therefore they bend less/more sharply at the boundary and similarly larger/shorter wavelengths higher frequency that would be bluer light or violet light tends to have a smaller/bigger refractive index which means it bends more/less sharply so you can imagine how

the differences are tiny but when spread out enough you can actually visibly detect those differences normally dispersion happens where longer wavelengths which is the redder side of visible light carry smaller refractive indices and therefore they bend less sharply at the boundary and similarly shorter wavelengths higher frequency that would be bluer light or violet light tends to have a bigger refractive index which means it bends more sharply so you can imagine how -as the wavelength increases or alternatively you could also say the refractive index goes up as the frequency increases so that means that the red wavelength of light typically doesn't bend as sharply at the air to glass boundary

Focal length importance? explain. Symbol?

the distance from the focus to the mirror is called the focal length and it's shown here we call it lowercase f the focal length will be an incredibly important piece of information to understanding how curved mirrors behave it's one of the most important things to know when dealing with a curved mirror what is its focal length

Explain antennae with Maxwell/ampere's law

the electric field here you saw the electric field was oscillating up and down because the charges were moving up and down the rod but in this orientation it also makes a time-varying magnetic field too that's part of ampere's law that's one of maxwell's equations if you make an electric field that changes with time you must make a magnetic field that changes with time as well the magnetic field that this charge creates no surprise it's oriented at a right angle to where the charge was moving because that's how electric charges make magnetic fields their magnetic fields point at right angles to where they were going so you have to imagine that this charge was moving up and down the rod and in outward directions you're making an electric field that oscillates up and down and you make a magnetic field that oscillates left and right and together they make a wave that self propagates as e changes it makes a changing b as a b changes it makes a changing e and this process continues forever in an expanding ripple in all directions again i'm only showing it to you horizontally here but it happens in all directions like a bubble

in which direction will the coil's own induced magnetic field point during the event? More (or stronger) rightward magnetic field vectors are penetrating the loop during this event

the loop fights back in opposition by creating a magnetic field that points to the left to try to cancel them out to preserve the amount of magnetic flux it previously had before the magnet moved.

Define amplitude? symbol?

the maximum deviation from average in both E and B fields as EM wave moves A the electromagnetic wave comes through the electric field oscillates and at its most extreme the peak how far away is it from what its average value is its average value might be zero or it might be offset from zero by some amount but whatever it is how extreme does the electric field strength get or the magnetic field strength and this that will be what we call its amplitude

the only way that you create your own magnetic field is? Explain?

the only way that you create your own magnetic field is you have to make a current flow the second right hand rule can help us backtrack to figure out which direction that current must have been remember it's very adaptable and it allows you to use your thumb as the magnetic field that the loop of wire creates inside the loop and your fingers can bend to show you the current that must have created it now coming full circle pun intended we are now ready to understand how those hydroelectric dams work that's actually how every electric generator works you change the magnetic flux through a coil wire it fights back by creating its own magnetic field to oppose that change and the only way that it can do that is to make a current flow and it's that current that we use to our advantage because we can use that to power anything we want everything from a simple light bulb to 16 percent of the world's energy usage we exploit Lenz's law and Faraday's law. we exploit it by provoking coils of wire into making currents flow and we use those currents to power the world

what is chromatic dispersion

the refractive index n for many transparent materials is different for every wavelength of light -when white light (made of all colors) meets a boundary between 2 materials, the bending happens at different angles for different wavelengths (colors) of the same light because each wavelength has its own (according to a refractive index of 1.5 in glass maybe for violet it's actually 1.51 and maybe for red it's actually 1.49)

the side that light can't actually go for that reason we treat the _______ length as a negative number. What mirror has this?

the side that light can't actually go for that reason we treat the focal length as a negative number convex

the speed of light it all happens because you're _______________ electric charges up and down that makes what?

the speed of light it all happens because you're accelerating electric charges up and down that makes an electric field that oscillates up and down and expands outward but that makes a magnetic field that oscillates left and right

What is image distance? Symbol?

there's another distance which is the distance from the image to the mirror the image is what you see in the mirror it's what you perceive to be on perhaps on the other side of the mirror in this case if you trace back the line of sight just like the cat trying to touch his friend you perceive a medicine bottle on the other side of the mirror a distance d i away from the mirror that's the image distance how far away does it appear the image is from the mirror it doesn't necessarily have to be on the back side it doesn't necessarily have to be behind the mirror in the case of flat mirrors that always happens flat mirrors always give you the impression that the image is behind the mirror but not every mirror does

these frequencies will correspond to different colors frequencies greater than this will exist as ________________ and frequencies less than this qualify as ________ all of these phenomena are collectively referred to as electromagnetic radiation

these frequencies will correspond to different colors frequencies greater than this will exist as uv radiation x-rays or gamma rays and frequencies less than this qualify as infrared radiation microwaves or radio waves all of these phenomena are collectively referred to as electromagnetic radiation

diverging lenses, well one thing that they have in common with converging lenses, which is? Why?

they don't just have one focus they once again have two foci and the reason is again the same light could come from either side

key feature of converging lens? how to draw?

they focus light by refraction so that it converges to a single point on the other side of the lens they're shaped in this teardrop like shape and when light comes in according to snell's law and you can draw the normal lines at the boundary you will see refraction happen so that the light gets converged to a single point on the other side now part of the assumption is that these light rays are parallel to the principal axis --they converge light

diverging lenses are always treated with a negative _________ anytime you see a diverging lens whatever its _______ appears to be we treat it as a negative distance. This is like concave/convex mirrors?

thing that will remind you of convex mirrors diverging lenses are always treated with a negative focal length anytime you see a diverging glands whatever its focal length appears to be we treat it as a negative distance

this spectrum where left represents ______frequency, ______ wavelength and right represents ________ wavelengths and ________ frequencies. Which is more dangerous for health?

this spectrum where left represents high frequency short wavelength and right represents longer wavelengths and lower frequencies --most dangerous for your health notice that it says higher energy light can be found on the left of this diagram along with higher frequency doesn't the really fast oscillation kind of look a little more dangerous ---ultraviolet x-rays gamma rays

Which of the following shows the induced current in this loop of wire at each of the three labeled points in space? (pic) A: outside magnetic field B: entering magnetic Field C: In magnetic Field

uOnly while the magnetic flux is changing does the wire react. uAt Point A, the magnetic flux through the wire is not changing (it's zero and it stays zero), so no current flows here. uAt Point B, the flux is changing quickly (from zero to a lot), so a current flows here. uAt Point C, the flux is no longer changing (it's a lot and it stay a lot), so no current flows anymore.

-You can't have a magnetic field created by this wire unless there are _______ in the wire. -How to find the direction of the current. Explain

uYou can't have a magnetic field created by this wire unless there are moving charges in the wire. -The direction of the current comes from the special version of RHR2 (most useful for loops of wire; thumb is the magnetic field inside the loop, fingers bend as current). uOnly a CCW current could've made this induced field.

What is the wave speed? equation? symbol? units? Vacuum?

v = λ x f In vacuum: v=c symbol: c The speed at which the wave propagates through space (m/s) --the speed that a wave propagates through space and the relationship between the speed that the wave moves and its wavelength and its frequency is a product you'll even notice that the units work out exactly like you think they would a wavelength in meters multiplied by a frequency per second gets you a speed meters per second --wave speed does measure a distance over a time ---when it comes to electromagnetic waves that speed at least in a vacuum is c c is the speed of light it's about three hundred million meters per second

What is a virtual image?

virtual images only appear when light rays seem as if they are diverging from somewhere where they couldn't light rays are impacting this curve mirror which you'll note is curved in a different way and they all spread out as they leave they don't look like they converge on any one location you can't trace them as all arriving at the same place but it does look as if they came from the same place virtual images always appear behind a mirror just like the cat trying to reach through the mirror to touch his friend which is actually himself virtual images are always visible in what appears to be mirror land on the other side of a glass mirror virtual images are not made by actual light rays converging in real space on the front side of a mirror they are only the appearance that light rays are coming from behind the mirror and if you trace each light ray back its line of sight that it originates in a place that it actually couldn't have gone or from which it could not have come so that's the difference between real and virtual images

waves move at speed v=λ⋅f, and for EM waves in a vacuum, ________ for all wavelengths/frequencies.

waves move at speed v=λ⋅f, and for EM waves in a vacuum, v=c for all wavelengths/frequencies.

we still want to draw a ray that goes in in the same direction as the center of curvature the problem is we can't get to the center of curvature so a ray that goes in line with the center of curvature bounces off the concave or convex mirror in line with the center of curvature it just bounces straight off again it can't get to point c

we still want to draw a ray that goes in in the same direction as the center of curvature the problem is we can't get to the center of curvature so a ray that goes in line with the center of curvature bounces off the convex mirror in line with the center of curvature it just bounces straight off again it can't get to point c

we're gonna treat light as if it's made of _______1_ _________ even though it's a wave that may spread out in all directions any one point on that wave moves roughly in a ____1__ ______ as long as it's in a single material

we're gonna treat light as if it's made of straight line rays even though it's a wave that may spread out in all directions any one point on that wave moves roughly in a straight line as long as it's in a single material

What is chromatic Aberration

when white light which is comprised of all colors gets incorrectly refracted depending on which color which wavelength of light it is so ideally all colors from the same white light would meet at the same location on the other side of the lens all the rays should get bent to this location and clearly in this picture they don't and when they don't the colors look blurry and smeared like this the reason that this happens is called chromatic dispersion

when you see that the electric field just changed then you'll know that an electric charge was?

when you see that the electric field just changed then you'll know that an electric charge was oscillated or accelerated or something something about its motion had to have changed

Why is Faraday's Law the only thing that can cause charges to suddenly start moving when they weren't before? What about Lorentz forces? electric fields? Magnetic fields?

while the magnetic field is increasing in strength the magnetic flux through this wire loop is also increasing and when that happens you induce a current but we didn't do it by moving the wire and as long as the flux was changing we got a current but when the flux stops changing because the magnetic field stops growing in strength the current stops too magnetic fields can only push charges that are already moving and these charges were totally stationary they just suddenly turned into becoming a current so it cannot be magnetic fields and it can't be lorentz forces that are directly responsible for driving this current because none of these charges were moving and lorentz forces can only push things that are already moving so someone else must be responsible for this at least directly responsible i know what you're thinking it was the magnetic field strength that increased right we made a stronger magnetic field but you're out of options when it comes to magnetic fields pushing charges because the only way they do it is the lorentz force and the only way the lorentz force can push something is if the charge is already moving so although the magnetic field strength got stronger there must be something else that is more directly the cause of this current that began out of nowhere the only culprit that we can blame the only thing that we know of that can suddenly push electric charges into moving when they weren't before is the coulomb force and that's caused by electric fields but we've only ever seen electric fields that are created by individual charges we call those electrostatic fields these charges cannot push themselves into motion sure they have electric fields each one of them does and sure they do push and pull on each other all the time but they're sitting here stationary this is electrostatic equilibrium everybody's happy they're just at rest if they were going to push each other into motion they would have done it by now so as we're checking down the list of possible suspects magnetic fields are out from the beginning they could not have done this electric fields are the only thing that we know of that could cause charges to start moving but it can't be the simple electrostatic fields that these charges already use to push on each other because they've already settled down that's why they weren't moving to begin with

when do you get the most/least amount of magnetic flux in loop of wire?

you get the most when the area vector and the magnetic field align -cosine of zero is one that gets you the most flux -you get less when the magnetic field vector and the area vector don't perfectly align (ex: 45 degrees cosine is less than 1 in that situation) - the least when they're oriented 90 degrees relative to each other cosine of zero is one but cosine of 90 that's zero cosine should measure 0 at 90 degrees

What is object distance? symbol?

you have a bottle in front of a flat mirror maybe it's like a medicine cabinet and this medicine bottle has light that emanates off of the bottle cap and it bounces off the medicine cabinet mirror and it hits your eyes what you'll notice about these rays is that they do look like they are diverging they don't look like they're heading to one location to meet at a point the distance from the object to the mirror itself we gave that a name and we call it d o distance object that's the distance from the object to the mirror and when i say the object i mean the thing that's making the image that you can see in the mirror the thing you're looking

What is the problem with motional emf. Explain.

you're going to grab this wire loop with your hand and you're going to drag it to the left out of the magnetic field, before it's exited the field at all, all of these electric charges are being moved through an external magnetic field they're being moved because they're on the wire and the wire's moving so they're moving through this magnetic field whether they like it or not. They're moving, they have charge, and because they're in a magnetic field that means they feel a lorentz force (met all three requirements so these electric charges feel the lorentz force) they're all moving to the left and the magnetic field points into the screen so they all need to feel a lorentz force that points down (right arm should go to the left, your fingers should point into the screen and that means your thumb has to point down) they're all experiencing the same motion and so they all wind up getting the exact same lorentz force now as of right now this doesn't do much because they don't really get any actual movement out of this force that's now pulling on them any more than the movement they're already experiencing. by marching along with the wire itself some of these forces are trying to pull charges in directions they can't even go. like any charge that is on the upper or bottom segment of this wire loop is being dragged in a direction where there is no wire loop below it. it can't go down. i'm going to ignore all the forces that are trying to pull charges in directions they can't even go and i'm only going to leave the ones that are being pulled in directions they actually could go along the wire these remaining lorentz forces could compel the charges to start moving but the charges would just run into each other and then they would coulomb repel each other back to where they came from. there really isn't anywhere to go here remember the charges are already moving to the left so if you're wondering how can a lorentz force compel a charge to start moving, what i really mean is it can start moving downwards but it's already moving to the left because the whole wire loop itself is being dragged to the left but again if both sides of this wire are having charges being pulled downwards there's nowhere to go they're just going to run into each other so that doesn't do much and you might as well not pay attention to those forces because they apparently are not responsible for making any current flow during this part of the journey (no current flow). as the left edge of this wire loop starts to make its way out of the magnetic field the left edge of the wire is now peeking out and that means that those charges are no longer in the presence of a magnetic field and so they can't feel lorentz forces anymore but everyone else can all the others are still moving to the left and the magnetic field that they're located in still points into the screen so they still get a lorenz force that points down but only the ones still in the magnetic field some of these forces still try to make the charges move in directions they can't actually go and i'm not going to pay attention to them but what you'll notice is that the remaining charges that actually feel lorentz forces are unopposed and they can bully their way around this circuit if they want there's nobody to stop them anymore so they feel a lorentz force that bends their trajectory downwards as the wire moves to the left and when they get pushed down they start pushing everyone else around (they will apply coulomb forces to the stationary charges) again they're unopposed nobody can stop them anymore and so that is effectively a current and it only began when one edge of the wire started to peak outside the magnetic field that left one side completely unopposed to start pushing everyone else around now eventually the right edge of the wire is also going to exit the magnetic field and when it does nobody will be feeling lorentz forces anymore and at this point with no more forces compelling them to keep moving their random collisions and coulomb repulsion will just stop all their motion and the current will come to an end even if you continue to drag the wire to the left more and more there's no lorentz forces to push charges so we see that a current only happens while the magnetic flux through this wire loop is changing that's exactly what you just witnessed and the current points in exactly the direction that lenses law would have predicted the current only begins when the leftmost edge of the wire loop starts to exit the magnetic field that's when its flux starts to change and the current ends when the rightmost edge of the wire loop exits the magnetic field that's when its magnetic flux stops changing so with less magnetic flux pointing into the loop as it exits the field it tries to compensate for that it doesn't like its magnetic flux being changed in particular being reduced and so it tries to make more magnetic flux point into the screen to make up for what it lost if you want to know which way that current would go point your thumb into the screen and you will see that it must make a clockwise current and it stops as soon as the last piece of the wire loop exits the magnetic field and the flux no longer changes

you're looking at is actually the back side of the mirror on the left the front side of the mirror is now on the right real light rays can't pass through point c and point f because they can't get to the other side they can't get through the reflective glass the reflective side of the mirror is the right side in concave/convex

Explain Visible Light

§The only part of the EM spectrum we can actually see directly with our eyes (4×〖10〗^14 Hz to 8×〖10〗^14 Hz). §Sir Isaac Newton subdivided this into seven colors (although it's a continuous spectrum). §Visible light is generally produced by molecular vibrations/rotations and atomic excitations/energy transitions. §Almost all light-sensitive life on earth uses some/all the visible range to see or for food (e.g., photosynthesis).

Do you know of any benefits to humanity from 1.) Ultraviolet, 2.) X-Rays, and/or 3.) Gamma Rays? Preface your answer with the numbered label (1 - 3) of the band you'll discuss.

§Ultraviolet light exposure of ten minutes can help produce enough Vitamin D to prevent common illnesses. §X-Rays are the basis of radiology because they easily penetrate soft tissue and reflect off dense bone matter. §Gamma Rays are often the emission result of radioactive nuclei. §Their extreme penetration of matter at the atomic scale and destruction of all life make them well suited for sterilization of microorganisms, as well as targeted treatment of some aggressive cancers.

Assuming n_1>n_2, TIR occurs at a critical incident angle of θ_1=θ_c because the refracted angle becomes θ_2→___ üTherefore, according to Snell's Law, TIR occurs when: ____________

üAssuming n_1>n_2, TIR occurs at a critical incident angle of θ_1=θ_c because the refracted angle becomes θ_2→90° (parallel to boundary) üTherefore, according to Snell's Law, TIR occurs when: n_1sin⁡〖θ_c 〗=n_2sin⁡〖90°〗

Because this incident ray is beyond the critical angle, only eyes ________ the water will see the fish, because light from the fish will never reach the outside air at this angle.

üBecause this incident ray is beyond the critical angle, only eyes below the water will see the fish, because light from the fish will never reach the outside air at this angle.

üLight coming from the top of the fish will undergo TIR at the water-to-air boundary üAll this light (from the top of the fish) will reach the swimmer's eyes, and the swimmer will see the top side of the fish by looking up at the point of reflection ü it makes it look like the fish is ___________ at the top of the water level

üLight coming from the top of the fish will undergo TIR at the water-to-air boundary üAll this light (from the top of the fish) will reach the swimmer's eyes, and the swimmer will see the top side of the fish by looking up at the point of reflection üThis is spooky; it makes it look like the fish is upside down at the top of the water level

Using the simulation, adjust the broadcast tower's Transmitter Movement from "Manual" to "Oscillate." Ensure that the Field Display Type is "Curve with Vectors." •What does the curve represent?

üThe curve shows the magnitude and direction of the (radiated/propagated) electric field created by the oscillating charges on the broadcast antenna üThe bigger the height of the curve (and E ⃗ vectors creating it), the stronger the Coulomb Force F ⃗_E=q⋅E ⃗ on a nearby charge q present for this oncoming wave in the E ⃗-field.

In which direction will this wire loop generate an induced magnetic field? Bar magnetic moving up/away from the loop. The loop must generate a current in order to create the opposing magnetic field. In which direction will this induced current flow? (pic)

üThe magnetic flux through the loop is decreasing. üThe loop responds by opposing this change. üThe opposite of less is more. üIt creates B ⃗_induced pointing down through middle of the loop to compensate. üCreate B ⃗_induced pointing down through middle of the loop with your thumb üLet your fingers bend around to see the induced current that would've made it. üThat's CW from above.

The magnification of the image is always given by? •What does the minus sign mean? •What does it mean that M<1?

üThe magnification of the image is always given by M≡h_i/h_0 =(-1.1 cm)/(1.8 cm) = -0.61 •What does the minus sign mean? üThis represents an inverted image because it's negative •What does it mean that M<1? üThis means that the image is smaller than the object üBecause this is a concave spherical mirror, we have another way of calculating the magnification: M = -d_i/d_o = -(5.5 cm)/(9 cm) = -0.61 üThis is identical to the ratio of the heights

The swimmer can only see the fish if his/her eyes are _____ the water-to-air boundary if the light from the fish is coming from an incident angle of _______.

üThe swimmer can only see the fish if his/her eyes are below the water-to-air boundary if the light from the fish is coming from an incident angle of θ_1≥θ_c.

What must be true regarding n_1 vs. n_2 if light is to be totally internally reflected at the boundary?

üTotal Internal Reflection can only occur when n_1>n_2, and never when n_1≤n_2. üThe reason is: to see TIR occur, the refracted light must be bent so little towards the normal line as to be almost parallel to the boundary üThis only occurs when light enters a less refractive medium so that it can be bent less towards normal

Magnetic Flux Equation? What is magnetic flux dependent on (equation symbols)?

Φ = B⋅A ⋅cos θ magnetic flux = flux density x area cut. Unit: Weber (Wb) -how strong the magnetic field is -how much area of a loop it can penetrate -the cosine of a certain angle

What is true regarding the refracted angle θ 2 when TIR begins?

θ 2 → 90

For the radio wave broadcast antenna in the simulation(wave up and down), which of the following orientations of the receiver antenna will pick up the signal? vertical receiver? North south horizontal receiver? east-west horizontal receiver?

•For the radio wave transmitter in the simulation, which of the following orientations of the receiver antenna will pick up the signal? üOnly the vertical antenna will work in the scenario shown here. üThe broadcast tower makes oscillating E fields that are vertical, and it is the E field that pushes the charges up and down in the receiver, so only a vertical antenna will be affected by the vertical E fields; the magnetic component isn't what does it

What exactly happens that causes a radio wave to be detected by a receiving tower? Explain the physical process of "detecting" an electromagnetic wave from the perspective of free electric charges on the receiving tower.

•How does the antenna work to detect this electromagnetic signal produced when radio stations broadcast? üWhen the broadcast electromagnetic wave arrives at the receiving antenna, the electric field oscillations apply Coulomb forces to the free charges on the receiver. üThis causes them to accelerate up and down (in our simulation) with the wave. üThe very act of them moving on the receiver is, by definition, a current, which can be interpreted as information.

In general, what exactly happens that causes a radio wave to be broadcast into space from a broadcast tower? Explain the physical process of creating an electromagnetic wave from the perspective of free electric charges on the broadcast tower.

•How is the radiating electric field (or electromagnetic signal) produced when radio stations broadcast? üFree electric charges (in reality, valence electrons) on the broadcast antenna are accelerated up and down üTheir acceleration causes ripples in the electric field (which makes ripples in the magnetic field too, even though we can't see it in this simulation) üThese ripples propagate outward in the form of electromagnetic waves to be received later

If the frequency of the broadcast tower decreases by a factor of two, it will now take longer for the electromagnetic wave to reach the receiving antenna. True or false? Explain.

•If the frequency of the transmitting electron decreases by a factor of two, it will now take longer for the electromagnetic signal to reach the receiving antenna. üFalse, because the speed at which the electromagnetic wave moves through space doesn't depend on how fast the broadcast antenna oscillates its charges. Try it yourself; you'll see. üNo matter how fast you oscillate the charges, it always takes the same amount of time for that wave to travel from the broadcast to the receiver

If the oscillation frequency of the transmitting electron decreases, the oscillation frequency of the electron in the receiver is instantaneously affected. True or false? Explain

•If the oscillation frequency of the transmitting electron decreases, the oscillation frequency of the electron in the receiver is instantaneously affected. üFalse, because even if we change the frequency of the broadcast antenna, it takes time for the ripples/waves in the electric and magnetic fields to reach the receiver antenna üOnly when the new waves reach the receiver will the electrons in the receiver antenna react accordingly

•In _________light attempts to cross a boundary between two different materials but fails to escape the first medium.

•In "Total Internal Reflection," light attempts to cross a boundary between two different materials but fails to escape the first medium. •It's all reflected at the boundary.

It's possible to receive a signal from the magnetic component of the EM wave if the receiving antenna is a loop of wire, instead of a straight wire. True or false? Explain

•It's possible to receive a signal from the magnetic component of the EM wave if the receiving antenna is a loop of wire, instead of a straight wire. üTrue! üIt is possible if the magnetic component of the EM wave arrives and the loop is oriented so that the B ⃗-field oscillates in and out of the area the loop antenna encloses.

In which of the following scenarios is TIR possible? •Light moving from air into glass •Light moving from water into air •Light moving from air into empty space •Light moving from glass into water

•Light moving from air into glass üTIR requires that n_1>n_2; this would never occur because n_1<n_2 for air-to-glass. •Light moving from water into air •Light moving from air into empty space •Light moving from glass into water üThe rest of these scenarios involve n_1>n_2; they all permit TIR as a possibility (under the right conditions)

Which of the following most closely matches the image created by this mirror for this object? Is the image real or virtual?

•Rays from the top of the candle intersect below the principal axis, so they must also illustrate the top of the candle wherever they meet •The image of the candle (as seen in the mirror) appears shorter than the actual candle (the object), and inverted. üWe know it's a real image because actual light rays converge to one spot in real space to form that image. üThe rays do not appear to diverge from behind the mirror üFun facts: 1.Real images can be projected onto screens (because they're created by real light rays that can be aimed at a wall) 2.Real images are always inverted. ü

If light is leaving water (n = 1.33) and entering air (n = 1.00): The light will bend more/less toward normal line? Where ancestor aim spear fish?

•Refractive index of water bigger than for air •Light ray in water bend "more" •Bend more towards perpendicular •Just as predicted •Aim below. •Fish dinner.

What is the speed of light inside Mystery A? chose Material 1 to be air (n_1≈1.00) •I aimed the light at θ_1=60° at the boundary between air and Mystery A. I measured that the refracted angle was θ_2=21°.

•So, according to Snell's Law of Refraction: n_1 sin⁡〖θ_1 〗=n_2 sin⁡〖θ_2 〗→n_2=n_1 sin⁡〖θ_1 〗/sin⁡〖θ_2 〗 ≈2.42 •Therefore, n_2=2.42≡c/v_2 →v_2=1/n_2 ∙c=▭0.41c

The electromagnetic waves generated by the broadcast tower produce currents in the receiving antenna. True or false? Explain

•The electromagnetic waves generated by the transmitting antenna produce currents in the receiving antenna. üTrue! üThat's exactly what happens: the incoming EM wave has an electric field component that pushes charges up and down on the receiver antenna üThe moving charges on the receiver are a current üThe current is interpreted as a signal

The electron in the receiving antenna oscillates at a lower frequency than the electron in the broadcast antenna (because of the distance between the antennas). True or false? Explain

•The electron in the receiving antenna oscillates at a lower frequency than the electron in the transmitting antenna because of the distance between the antennas. üFalse, because the free charges in the receiver antenna clearly do not oscillate at different frequencies than the broadcast antenna (we can measure this). üThey get pushed up and down by the exact same electric field that was created by the broadcast antenna, so why would they oscillate at a different frequency?

•We know it's a ___1____ image because ___2____ light rays do not converge •They only appear to diverge from in front of the lens. •Remember, ____1_____ images: •Are always upright •Only appear on the ____1_____ side of the lens •Can/Cannot be projected.

•We know it's a virtual image because real light rays do not converge •They only appear to diverge from in front of the lens. •Remember, virtual images: •Are always upright •Only appear on the virtual side of the lens (the front side) •Cannot be projected.

We know that higher/lower frequencies tend to refract more/less in dispersive materials, so violet bends the most/least toward normal •Red is the visible light with the lowest frequency (and largest wavelength), so it bends the least/most

•We know that higher frequencies tend to refract more in dispersive materials, so violet bends the most (meaning, toward normal) •Red is the visible light with the lowest frequency (and largest wavelength), so it bends the least.

What are some ways that you can you ensure that light does not refract at all at the boundary between two media?

•What are some ways that you can you ensure that light does not refract at all at the boundary between two media? •There are two different ways to prevent refraction at a material boundary: 1.Aim the light with θ_1=0°. 2.Ensure that n_1=n_2.

When light leaves a less refractive medium and enters a more refractive medium, does the light bend more or less towards the normal line at the boundary?

•When light leaves a less refractive medium and enters a more refractive medium, does the light bend towards normal? •The light bends more (toward normal) in more refractive media. •This means that n_2>n_1. You can see that θ_2 is clearly smaller than θ_1 because the refracted ray is bent closer toward the normal line.

When \theta_1 =45 degrees as light travels from air into Mystery B, calculate the angle of refraction theta_2 via Snell's Law.

•When θ_1=45° as light travels from air into Mystery B, calculate θ_2 via Snell's Law. •According to Snell's Law: n_1 sin⁡〖θ_1 〗=n_2 sin⁡〖θ_2 〗 →sin⁡〖θ_2 〗=n_1/n_2 sin⁡〖θ_1 〗 •So, θ_2=sin^(-1)⁡(n_1/n_2 sin⁡〖θ_1 〗 )= sin^(-1)⁡(1.00/1.41 sin⁡(45°) ) =sin^(-1)⁡(1.00/1.41∙0.707)≈▭(30°)

Will this bulb light up when the EM wave approaches its antenna? Bulb is horizontal

•Will the bulb connected to this receiving antenna glow in each of the following cases? •No, because the antenna is aligned with the magnetic component of the EM wave, which is useless here •The electric component can't push charges up and down on a horizontal receiver antenna

Will this bulb light up when the EM wave approaches its antenna? bulb is vertical

•Will the bulb connected to this receiving antenna glow in each of the following cases? •Yes, because the (vertical) electric component of the EM wave can oscillate charges on the (vertical) receiver antenna •The magnetic component plays no role in this event.

____________ is a function that provides the angle θ whose sine is x •There is no angle whose sine is bigger than _; sine can't be bigger than __ •Therefore, sin^(-1)⁡(n_2/n_1 ) is _______ when n_2>n_1, as that means n_2/n_1 >1

•θ=sin^(-1)⁡(x) is a function that provides the angle θ whose sine is x •There is no angle whose sine is bigger than 1; sine can't be bigger than 1 •Therefore, sin^(-1)⁡(n_2/n_1 ) is undefined when n_2>n_1, as that means n_2/n_1 >1

What is the equation for the rate that the magnetic flux changes causes an effective induced voltage in the wire, and that induced voltage acts like a battery?

∆V(induced)= - ∆Φ/∆t ∆V(induced)= - ∆Φ_(B)/∆t Faradays law on induction

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