Phsyics Midterm 3
For small angles, sin θ ≈ tan θ and, when using radians, sin θ ≈ tan θ ≈ θ. so When is it ok to use the small angle approximation?
"Small" θ means that θ << 1 (in radians) - how much less than one depends on the accuracy desired. • For 2 sig. fig. accuracy (good enough for this course), you need θ < 0.3 (radians), or θ < 15˚. • If you're in doubt, go ahead and use it, and check at the end to make sure the angle is actually small. • Usually, you're safe for m <≈ 10-20
what does a positive value of m and a negative value of m mean
+=image is upright -=image is inverted
what is a ray source
-A light ray is an idealization. There are no true ray sources. However, the thin beam of a laser is often a good approximation of a single ray.
what is true about diverging lens
ALWAYS makes virutal images
how do all EM waves travel
All electromagnetic waves travel in a vacuum at the speed of light:
what is true
An atom is more complicated than a simple one-dimensional box, but an electron is "confined" to an atom
why ca light overlap
Because light acts as a wave, light waves can overlap and interfere constructively and destructively. • We use very small slits to create waves that can interfere with each other. • When the light wave passes through the slit, it diffracts.
what did rutherford discover
Beta rays and Alpha rays. Soon afterward, Paul Villard discovered another type of ray that could be emitted, which Rutherford named Gamma rays.
what is a parallel ray source
Certain sources, such as flashlights and movie projectors, produce a bundle of parallel rays. Rays from a very distant object, such as a star, are very nearly parallel.
when will destrcutive interference occur
Destructive interference will occur when the light waves occur at positions on the screen for which r1 and r2 differ by a whole number of wavelengths plus half a wavelength (m+1/2)lamda Destructive interference is seen as a lower intensity of light on the viewing screen (dark fringes).
The integer m is called the order of diffraction.
Difference from double-slit interference: There are no corresponding equations for destructive interference Don't use the small angle approximation (θm is not small)
what are spectal lines
Each line in a discrete spectrum is called a spectral line and represents one specific wavelength
what is important to reme
Every wavelength that is absorbed by the gas is also emitted, but not every emitted wavelength is absorbed.
what happens if we apply an postivie voltage
If we now apply enough positive voltage to the anode, it will attract all of the ejected electrons to the anode. Any further increase in ΔV does not cause any more electrons to reach the anode and thus does not cause a further increase in the current I.
Einstein suggested that electromagnetic radiation consists of photons,
Light of frequency f consists of discrete quanta, each of energy E = hf. Each photon travels at the speed of light c. Light quanta are emitted or absorbed instantly on an all-or-nothing basis. A photon cannot be "partially absorbed". Each light quantum, when absorbed by a metal, delivers its entire energy to one electron.
how does light spread
Light spreads out behind each slit. • As with the sound waves, constructive interference occurs at a point where the distances r1 and r2 from the slits differ by a whole number of wavelengths
The angular size of the object when using the magnifier is larger than without the magnifier by a factor of
M=theta/thetha0 thehta0=theta/25 M is angular mag
Doubling the intensity of the light ( ) doubles the
Number of photons per second Number of electrons ejected per second The current ∆q/∆t.
what is the ionization limit
On the left is the energy-level diagram of the Bohr Hydrogen Atom The lowest rung on the diagram is the ground state The top rung on the energy-level diagram is called the ionization limit. This is the energy required to free an electron from the nucleus
how is energy quantized
Since particles have wave-like properties, we consider a wave reflecting back and forth from the ends of the box. The reflections will create a standing wave, analogous to the standing wave on a string that is tied at both ends.
summary
Summarizing: The energies are quantized. Only certain energies are allowed; all others are forbidden. This is a consequence of the wave-like properties of matter. The ground state is stable. Quantum systems seek the lowest possible energy state. A particle in an excited state, if left alone, will jump to lower and lower energy states until it reaches the ground state. Quantum systems emit and absorb a discrete spectrum of light. Only those photons whose frequencies match the energy intervals between the allowed energy levels can be emitted or absorbed. This is a consequence of the particle-like properties of light.
The magnification m = -s'/s is positive since the virtual image is upright.
That means that s' is negative
where are the dark fringes located
The dark fringes are located exactly halfway between the bright fringes
what does the iris do
The iris determines how much light enters the eye, like the diaphragm of the camera.
what is the visible spectrum
Visible light wavelengths range from 400 nm-700 nm. this is the visible spectrum
what is discrete spectrum
When we do this, we find the emitted light contains only certain discrete, individual wavelengths. Such a spectrum is called a discrete spectrum.
Electrons convert kinetic energy to potential energy as they slow down. ΔU = -eΔV = -ΔK
When ΔV = -ΔVstop, the current ceases and the fastest electrons with Kmax are being turned back just as they reach the anode. 100% of their kinetic energy is converted to potential energy, so
what is scattering
a process in which single rays are broken into many weaker rays that leave in all directions.
what are beta rays
are actually high-speed electrons.
why is n always greater than 1
n is always greater than 1 because v is always less than c. A vacuum has n = 1
The speed of light in a material is characterized by the material's index of refraction n, defined by
n=speed of light in a vaccum/speed of light in a material
m=
s'/s
If ΔV is negative
the current drops until ΔV = -Vstop , where the current is zero. Vstop is called the stopping potential.
when delta v is equal to zero
the electrons leave the cathode in all directions, only some reach anode
for a near point
the eye focuses on close objects, the cillary muscles are contracted and the lens is more curved
for a far point
the eye focuses on distant objects, the cillary muscles are relaxed and lens is less curved
when does Destructive interference (a dark fringe) occurs when
Δr = (m + 1/2) λ m = 0,1,2,3
The condition for constructive interference for a diffraction grating (N light waves, from N different slits), is exactly the same as for just 2 slits.
𝑚𝜆=𝑑𝑠𝑖𝑛𝜃_𝑚,𝑚=0,1,2,3,...
The position ym of the mth bright fringe is
𝑦_𝑚=𝐿𝑡𝑎𝑛𝜃_𝑚,𝑚=0,1,2,3,...
what are the impications of the bohr model
- Matter is stable. Once an atom is in its ground state, there are no states of any lower energy to which it can jump. It can remain in the ground state forever. -Atoms emit and absorb a discrete spectrum. When an atom jumps from an initial state with energy Ei to a final state with energy Ef, conservation of energy requires that it emit or absorb a photon with energy -Emission spectra can be produced by collisions. Energy from collisions can kick an atom up to an excited state (this is called collisional excitation). The atom then emits photons in a discrete emission spectrum as it jumps down to lower-energy states. -Absorption wavelengths are a subset of the wavelengths in the emission spectrum. Just like any system with quantized energies, most atoms, most of the time, are in their lowest energy state, and so the absorption spectrum consists of only those transitions such as 1 → 2, 1 → 3, etc... -Each element in the periodic table has a unique spectrum. The energies of the stationary states are just the energies of the orbiting electrons. Different elements, with different numbers of electrons and protons, have different stable orbits and thus different stationary states. States with different energies will emit and absorb photons of different wavelengths.
what happens to an object inside the focal point
-, a ray passing through the near focal point (on it's left in the diagram) is traveling away from the lens -The rays emerging parallel to the axis entered the lens along a line passing through the near focal point.
what is a diffraction grating
-A diffraction grating is a multi-slit device. -The waves emerge from each slit in phase. -Each wave will spread out and interfere with each other wave. -We can analyze the diffraction grating in a similar manner to what we did for the double slit interference experiment. -Let d be the distance between neighboring slits, and again let L be the distance from the slits to the screen. -Let N be the number of slits in the grating
what happens in a photon emission
-A quantum system in energy level Ei that jumps down to energy level Ef loses an energy ΔEsystem= |Ef - Ei|. -The jump corresponds to the emission of a photon with frequency f photon=deltaE/h
what is x ray diffraction
-A side view of x rays striking a crystal shows that most x rays are transmitted through the plane, but a small fraction of the wave is reflected. The reflected wave obeys the law of reflection. -There are many parallel planes of atoms in a solid. A small fraction of the wave reflects from each plane. -The net reflection from this solid is the superposition of the waves reflected by each atomic plane.
Shadows
-An opaque object can intercept rays from a point source, leaving a dark area, or shadow, behind it. -With a point source, the shadow is completely dark and the edges of the shadow are sharp. -An extended source is a large number of point sources, each of which casts a shadow. -The shadows overlap, so the overall shadow is no longer sharp. -Depending on the size of the source, there is often a true shadow that no light reaches, surrounded by a fuzzy region of increasing brightness.
The photon nature of light isn't apparent in most cases. Only at extremely low intensities does the light begin to appear as a stream of individual photons. The light sources with which we are familiar emit such vast numbers of photons that we are only aware of their wave-like superposition, just as we notice only the roar of a heavy rain on our roof and not the individual drops of water.
-Early light detectors consisted of a polished metal plate in a vacuum tube. When light fell on the plate, an electron current was generated that could trigger an action, such as sounding an alarm, or could provide a measurement of the light intensity -A solar cell works much like a battery, but the energy to lift charges to a higher potential comes from photons.
The photon model of electromagnetic waves consists of three basic postulates:
-Electromagnetic waves consist of discrete, massless units called photons. A photon travels in a vacuum at the speed of light. -Each photon has energy: Ephoton = hf f is the frequency of the wave and h is a universal constant called Planck's constant: h = 6.63 ´ 10−34 J ⋅ s The superposition of a sufficiently large number of photons has the characteristics of a continuous electromagnetic wave. -The total energy of a wave consisting of N photons is Since intensity I = P/A and power P = Etot/∆t, the intensity of light in the photon model is given by:
-Electrons are ejected from the cathode when they absorb an "energetic enough" photon. -Many electrons will reach the anode, creating a measurable current (but some do not).
-Electrons are ejected the instant they absorb a photon, so the current starts instantly.
why is green glass green what does colored glass do
-Green glass is green because it removes any light that is not green. -Colored glass absorbs all wavelengths except those of one color, which is transmitted through the without hinderance -Colored glass or plastic is a filter that removes all wavelengths except a chosen few. Opaque objects appear colored by virtue of pigments that absorb light from some wavelengths but reflect light of other wavelengths.
for photon emission
-If a quantum system changes from one state to another, its energy changes, but conservation of energy still holds. -So if a system drops from a higher energy level to a lower, the excess energy ΔEsystem must go somewhere. -Generally this excess energy leaves the system the form of an emitted photon.
who discovered the elctron
-In 1897 J. J. Thomson discovered the first subatomic particle: the electron (e-). -The mass of the electron is much smaller than the mass of the whole atom, so he thought an atom consisted of negatively charged electrons embedded in a more massive cloud of positive charge. This model is called the "raisin-cake model."
what is the ground state what is the excited state
-The lowest rung on the energy-level diagram, with energy E1, is the ground state. Higher rungs are called excited states and are labeled by their quantum numbers. n is the quantum number in the diagram shown.
what is diffraction
-The wave spreads out to fill the space behind the opening. -Diffraction happens to any wave passing through an opening, although it is not always noticeable
for converging lens
-There are focal points on both sides of the lens. -The focal point on the side from which the light is incident is the near focal point; the focal point on the other side is the far focal point. rays converge at the far focal point
what is a The magnifier lens is held such that the object is at or just inside the lens's focal point.
-This produces a virtual image far from the lens. -The location of the virtual image in a magnifier is convenient because your eye muscles are fully relaxed when looking at a distant object. The distant virtual image is what the eye focuses on with a magnifier.
what is total internal reflection
-Total internal reflection (TIR) occurs when a light ray is unable to refract through a boundary. Instead, 100% of the light reflects from the boundary. -Crossing a boundary into a material with a lower index of refraction, e.g. from glass to air, causes the ray to bend away from the normal. -As angle θ1 increases, the refraction angle θ2 approaches 90°. -The fraction of light energy that is transmitted decreases while the fraction reflected increases.
what is it about aosportion
-Typically, quantum systems exist in their ground state. When excited, they (fairly quickly) emit a photon (or photons) and return to their ground state. For this reason, absorption lines (usually) correspond to transitions from the n = 1 state only. When solving problems, you may always assume this, unless told otherwise.
the experimet
-We can design an experiment in which electrons moving along a y-axis pass through a slit of width a. -The slit causes the electrons to spread out and produce a diffraction pattern. We can think of the experiment in a different way - as making a measurement of the position of the electrons. As an electron goes through the slit, we know something about its horizontal position. We can establish an uncertainty, a limit on our knowledge. The uncertainty in the horizontal position is Δx = a, the width of the slit. After passing through the slit, the electrons strike the screen over a range of positions. The electrons must have acquired a horizontal component of velocity. By forcing them through a slit, we gained knowledge about their position, but that caused uncertainty in our knowledge of the velocity of the electrons
what happens when the wave opening is larger than the wavelenght
-When the opening is many times larger than the wavelength of the wave, the wave continues to move straight forward. -There is a defined region, the "shadow," where there is no wave. • This is similar to the straightline appearance of light with sharp shadows as light passes through large windows.
what happens with hyperopia
-With hyperopia, no amount of accommodation can allow the eye to focus on, e.g. an object 25 cm away. -But, the person can still see faraway objects with some accommodation of the eye.
what type of lens is used for nearsightness
-a converging lens forms a virtual imageat the eyes's near point. this image acts as an object for the eye and this is what the eye focuses on
plane mirrors
-point P¢, from which the reflected rays diverge, is called the virtual image of P. -The image is virtual because no rays actually leave point P¢, however the light waves act exactly as if they were. -The image distance s¢ is equal to the object distance s:
what are the three rays for a convex lens
1) a ray parallel to the axis and reflects as though it came through the focal point 2) a ray initially directed toward the focal point and relfects parallel 3) a ray that strikes to the center of the lens and reflects at an equal angle on the opp side of the optical axis
steps for a divergig lens
1) ray parallel to axis diverges (refracts) along a line through the near focal point 2) a ray along a line toward the far focal point emerges parallel (refracts parallel) 3) a ray through the center of the lens that does not bend
refraction tips on how to do it
1. draw ray diagram 2. draw a line perpendicular to the boundary (normal), do this at each point a ray crosses a boundary 3.show the light ray bending *the angle is larger on the side with the smaller angle of refraction
The Plane Mirror
1.Rays from each point on the object spread out in all directions and strike every point on the mirror. Only a very few of these rays enter your eye, but the other rays are very real and might be seen by other observers. 2. Rays from points P and Q enter your eye after reflecting from different areas of the mirror. This is why you can't always see the full image in a very small mirror.
what is the thin lens equation
1/f=1/s-1/s' *the sign is + for a converging/convex *the sign is diverging/concave
1. a plane wave is incident on the double slit 2. waves spread out behind each slit
3. constructive interference occurs whe r1 and r2 differ by a whole wavelength 4. the bright fringes are labelled by the integer m Constructive interference is seen as a higher intensity of light on the viewing screen (the bright fringes)
what is a lens
A lens is a transparent material that uses refraction of light rays at curved surfaces to form an image.
what does a lens with a higher refractive power mean
A lens with higher refractive power (shorter focal length) causes light rays to refract through a larger angle.
what does a nucleus contain
A nucleus contains Z protons plus N neutrons. The atom has a mass number A = Z + N. Proton and neutron masses are ≈ 1u: 1u = 1 atomic mass unit = 1.66 × 10-27 kg A × (1 u) is approximately the mass of the nucleus. We'll learn about nuclear masses in detail next chapter
A camera is a device that projects a real image onto a plane surface, where the image can be recorded onto photographic film or an electronic detector which records the image.
A pinhole camera is a lightproof box with a small hole punched in it. It has no lens. If the hole is sufficiently small, it allows only one light ray from each point of an object to enter the box.
what is a plane mirror
A plane mirror is a flat mirror. rays from p reflect the mirror
what is a point source
A point source is also an idealized source of light. It is infinitely small and emits light rays in every direction. The tiny filaments of these bulbs approximate point sources.
what is the thin lens app
A thin lens is an idealized lens whose thickness is zero and that lies entirely in a plane called the lens plane. Within the thin-lens approximation, all refraction occurs as the rays cross the lens plane, and all distances are measured from the lens plane. and we draw three special rays
what is a virural image
A virtual image is at a point from which rays appear to diverge, but through which no rays actually pass.
what are inteference fringes
Along the viewing screen, the difference Δr alternates between being a whole number of wavelengths and a whole number of wavelengths plus half a wavelength, leading to a series of alternating bright and dark bands of light -The central maximum is the brightest fringe at the midpoint of the screen
what does an electron have
An electron has an intrinsic angular momentum called the electron spin. Hence, it has an inherent magnetic dipole moment—it acts like a tiny bar magnet.
what is the ray model of light
An equally well-known "fact" is that light travels in a straight line. These straight-line paths are called light rays. • The properties of prisms, mirrors, lenses, and optical instruments such as telescopes and microscopes are best understood in terms of light rays. • The ray model of light, the basis of ray optics, is the subject of the next chapter
what are photons
An interference pattern made with very low intensity light shows that the light hits the screen in discrete "chunks" called photons.
Anayzled single silt
At points away from the center of the screen, interference occurs. Wavelets 1 and 2 start a distance of a/2 apart. If Δr12 is λ/2 then the wavelengths are out of phase and interfere destructively. If Δr12 is λ/2, then so are Δr34 and Δr56, so perfect destructive interference occurs.
summary
Constructive interference (a bright fringe) occurs when • Assuming L >> d, • So, at the values θm which satisfy the following, there is a bright fringe at the point with that θm: • The distance of this point from the center of the screen is: mλ = d sin θm Δr = mλ, m = 0,1,2,3,... Δr = d sin θ ym = L tan θ
what do corrective lens prescribe
Corrective lenses are prescribed by their refractive power: P=1/focal length units: The SI unit of refractive power is a diopter D: 1 D = 1 m-1 Note: 1 m-1 = 0.01 cm-1, and 1 cm-1 = 100 m-1.
An electron can escape after absorbing a photon if its energy exceeds the work function E0, i.e. if
Eelec=hf> or equal to Eo
what are Fiber Optics
Fiber optics use total internal reflection for the transmission of light through optical fibers. Light rays pass into the narrow- diameter glass fiber, but then strike the inside wall of the fiber an at angle of incidence approaching 90°. This is larger than the critical angle, so the light undergoes TIR and remains inside the glass. When the light rays reach the flat end of the fiber, the angle of incidence is lower and the light can cross the boundary. To protect it from external damage, a glass cladding surrounds the glass core. Light undergoes TIR at the cladding boundary, and remains within the core. Endoscopes made from optical fibers are used for anthroscopic surgery.
what is the work function
For any given type of metal, there are some electrons that are most weakly bound. Their binding energy is labeled E0. Many electrons will require an energy greater than E0 to escape, but all will require at least E0.
This is called x-ray diffraction.
For most angles of incidence, x rays reflected from the multiple atom planes of a solid are out of phase. At a few specific angles of incidence, the reflected waves are in phase. They interfere constructively to produce a strong reflection.
chloropyll absorbs most of the blue/violet and red light for use in photosynthesis
Green and yellow light are not absorbed, but instead are reflected, giving the object a greenish-yellow color. When you look at the green leaves on a tree, you're seeing the light that was reflected because it wasn't needed for photosynthesis.
What is Huygen's Principle?
Huygens' Principle has two parts: Each point on a wave front is the source of a spherical wavelet that spreads out at the wave speed. At a later time, the shape of the wave front is the curve that is tangent to all the wavelets. The curve tangent to the wavelets of a plane wave is a plane that has propagated to the right. The curve tangent to the wavelets of a spherical wave is a larger sphere.
what is a real image
If rays diverge from an object at point P and interact with a lens such that they converge at point P¢, then we call P¢ a real image of point P. The image is called an inverted image because it is upside down with respect to the object. This is a basic characteristic of real-image formation. Rays from point P fill the entire lens surface. A larger lens "collects" more rays, and therefore makes a brighter image The rays don't stop at P¢ unless we place a screen in the image plane. When we do, the image is sharp and well-focused. If the screen is placed other than in the image plane, an image is produced but it is blurry and out of focus.
If the electronic detector is located on the image plane, then a sharp image will form on it.
If the electronic detector is located in front of the image plane, the rays have not converged and would form a small blurry circle instead of a sharp point.
important
If the frequency f of a photon is less than f0 then none of the electrons will have sufficient energy to escape no matter the intensity of the light.
what is spectroscopy
If the light incident on a grating consists of two slightly different wavelengths, they will diffract at slightly different angles. If N is sufficiently large, two distinct fringes will appear on the screen.
important for concave
If the object is inside the focal point, the image is a virtual image.
**for Concave Mirrors
If the object is outside the focal point, the image is real because rays converge at the image point P′. If the object is inside the focal point, the image is a virtual image.
for seeing an objecT
In order for our eye to see an object, rays from that object must enter the eye. You cannot see a laser beam traveling across the room because no light from the laser enters the eye. The beam is invisible to you. This is the case for either a ray or a parallel ray source. A point source and an extended source emit rays in every direction, and some of the rays will enter the eye no matter where it is located. Thus a point source or an extended source is visible to all observers.
if an An electron inside a metal is bound.
In order to escape it must acquire an amount of energy equal to at least E0. An electron in a metal that gains energy hf from an incoming photon and then escapes, spends some of that energy to escape, and the remaining energy is all kinetic.
what is the bohr model
In the Bohr model, the electrons in an atom can exist in only certain allowed orbits. This is same situation we had for the particle in a box, where there were only certain allowed energies Basically, Bohr just added discrete energy levels to the classical model of the atom. A particular arrangement of electrons in these orbits is called a stationary state. -Each stationary state has a discrete, well-defined energy En, as the energy-level diagram shows. That is, atomic energies are quantized. The stationary states are labeled by the quantum number n in order of increasing energy: E1 < E2 < E3 < ...
what are photons
Individual photons pass through the double slit, as the image builds up, the photons are grouped into bands at exactly the positions we expect to see the bright constructive-interference fringes. We see particle-like dots forming wave-like interference fringes. If only one photon is passing through the apparatus at a time, it must interfere with itself to create the wave-like pattern. If each photon is interfering with itself (nothing else is present), then each photon, despite the fact that it is a particle-like object, must go through both slits, something only a wave could do. Sometimes light exhibits particle-like behavior and sometimes it exhibits wave-like behavior.
what are reflection gratings
It is more practical to make reflection gratings, like a mirror with hundreds or thousands of narrow grooves cut into the surface. The grooves divide the surface into many parallel reflective stripes, which spread the wave. The grooves are "effective" slits The interference pattern is exactly the same as the pattern of light transmitted through N parallel slits. The calculations determined for the diffraction grating applies to reflection gratings as well as to transmission gratings. The array of holes on a DVD is used to transmit data, but optically they cause the rainbow colors observed. The grooves in a CD disk are "effective" slits: the incident white light forms interference maxima for different colors at different angles. A spectrum produced by a grating is a result of different wavelengths interfering constructively at different locations.
what are x rays
It was determined that the x rays were electromagnetic waves with very short wavelengths. X rays are still produced by colliding fast electrons with a metal target. Substances with high atomic numbers, such as lead or the minerals in bone, are effective at stopping x rays. An x-ray image is created when x rays are sent through a part of the body lying on film. The dense tissues pass few x rays, so the film is not exposed in those regions. When the film is developed, the film is light where rays were blocked.
The bright central maximum at θ = 0 has the highest intensity.
L is the distance from the slit to the screen Using the small angle approximation, the dark fringes in the single-slit diffraction pattern are located at: The width w of the central maximum is defined as the distance between the two p = 1 minima, which is simply w = 2y1
Because L >> d, the two paths to point P are virtually parallel.
Let θ be the angle from the horizontal to the paths r1 and r2
what is dispersion
Light of a fixed wavelength has a definite color, but not vice versa! For example, if one sees light which is a combination of 650 nm and 550 nm, it appears yellow -Dispersion is the slight variation of the index of refraction with wavelength.
what are the three main functional groups of the eye
Like the camera, the eye has three main functional groups: An optical system to focus incoming light A diaphragm to adjust the amount of light entering the eye A light-sensitive surface to detect the resulting image
what does measuring the stopping potential do
Measuring the stopping potential tells us the maximum kinetic energy of the electrons.
-When UV light shines on the cathode, a steady counterclockwise current passes through the ammeter. -The incident light causes electrons to be ejected from the cathode at a steady rate. If we turn off the light, the current goes to zero
Moreover: -The current appears without delay when the light is applied. -The current I is directly proportional to the light intensity. If the light intensity is doubled, the current also doubles. -Electrons are emitted only if the light frequency f exceeds a threshold frequency f0. -The value of the threshold frequency depends on the type of metal from which the cathode is made.
A prism disperses light. Newton used prisms to study color.
Newton blocked all the rays of light from the first prism except for those of one color. Only that color was seen through the second prism and it was unchanged. Newton recognized that this meant the color is associated with light itself; the prism was not altering the properties of light.
what is refraction
Part of the light continues into the second medium. It is transmitted rather than reflected, but the transmitted ray changes direction as it crosses the boundary. The transmission of light from one medium to another, but with a change in direction, is called refraction.
what are rainbows due to
Rainbows exist due to the combination of reflection, refraction and dispersion of light as it interacts with the raindrops. The dispersion from one raindrop may lead you to think that the top edge of a rainbow is violet, but it is not. The rays leaving a single drop spread out and do not all reach your eye. A ray of red light that does reach your eye comes from a drop higher in the sky than a ray of violet light.
If the detector is located behind the image plane, the rays would be diverging and again create a blurry image.
Rather than move the detector, a camera is focused by moving the lens.
Orbiting electrons are very light, so a photon or a rapidly moving particle, such as another electron, can knock one of the electrons away, creating a positive ion.
Removing one electron makes a singly charged ion, qion = +e. Removing two electrons creates a doubly charged ion, q = +2e.
what was the first nuclear phsyics expt
Rutherford set up an experiment to probe the inside of an atom. He shot high-speed alpha particles through a thin gold foil. If the atom's structure were described by Thomson's raisin-cake model, then the forces exerted on the alpha particle by the positive atomic charges should roughly cancel the forces from the negative electrons, causing the particles to experience only slight deflections.
what is angle of incidence what is angle of refractio
The angle between the incident ray and the normal is the angle of incidence. The angle on the transmitted side, measured from the normal, is called the angle of refraction.
what is the There is an important difference between the intensity pattern of double-slit interference and the intensity pattern of multiple-slit diffraction grating.
The bright fringes of a diffraction grating are much narrower. As the number of slits, N, increases, the bright fringes get narrower and brighter.
What is hyperopia?
The cause of farsightedness, called hyperopia, is an eyeball that is too short for the refractive power of the cornea and lens.
what is myopia
The cause of nearsightedness, called myopia, is caused when the eyeball is too long for a fully relaxed eye to focus distant objects onto the retina. Rays from a distant object come to focus in front of the retina and have begun to diverge by the time they reach the retina But, the person can still focus on objects nearby when the eye is relaxed (and extremely close objects with accommodation). a fully relaxed eye focuses teh image in front of the retina, the image is blurry
for a plane mirror
The dashed lines indicate that the rays appear to have come from point P¢. All reflected rays appear to come from point P¢. The light rays appear to come from behind the mirror.
what are the pentration levels
The different types also have different abilities to penetrate solid matter - alpha particles are the most easily blocked, and gamma rays are the most penetrating.
what is the focal length
The distance of the focal point from the lens is called the focal length f of the lens.
analyzed
The double slit experiment consists of a double slit spaced d apart and a distance L to the viewing screen. • To determine the interference, we need to compute the pathlength difference, Δr = r1 - r2 • We assume L is much larger than d. (L >> d). They are related: y = L tan θ
what is true about energy of electrons in an atom
The electron orbits are, in some sense, standing waves, and the energy of the electrons in an atom must be quantized. Generally speaking, whenever any particle or object is confined to a certain region by any means, its energy levels are quantized.
what is the photoelectric effect
The emission of electrons from a substance due to light striking its surface is called the photoelectric effect.
Maximum Angular Size
The eye cannot focus on objects closer than its near point Normally the near point is about 25 cm. Typically the near point becomes longer as you get older Thus, an in-focus object at the near point has a maximum angular size θ0. From the geometry of the image, tan θ0 = h/25 cm. Using the small-angle approximation, we find
what is the far point
The far point (FP) is the most distant point on which the relaxed eye can focus. For normal vision, the FP is infinity.
what is important to remember about the frequency of a wave
The frequency of a wave does not change as the wave moves from one medium to another. The wavelength of light in a material is v/f
what is the focal point
The incoming rays initially parallel to the optical axis converge at the same point, the focal point of the lens.
The integer n is called the principle quantum number.
The integer l is called the orbital quantum number. the magnetic quantum number
The angle of incidence, θi, is the angle between the incident ray and the line perpendicular to the surface. The angle of reflection, θr, is the angle between the reflected ray and the normal to the surface.
The law of reflection states: The incident ray and the reflected ray are both in the same plane, which is perpendicular to the surface, and The angle of reflection equals the angle of incidence: θr = θi
Light is refracted by, in turn, the cornea, the aqueous humor, and the lens. The indices of refraction (n) in these parts of the eye differ somewhat, but average around 1.4. Most of the eye's refraction happens at the cornea due to its curvature and the large difference in the indices of refraction of air and the cornea.
The lens's index of refraction does not differ much from the fluid in which it is embedded. When the lens is removed (like for a cataract), the cornea alone provides a marginal level of vision.
what is a convex
The mirror shown to the right is a convex mirror. The parallel rays that reflect off its surface appear to have come from a point behind the mirror. Convex mirrors are similar to diverging lenses. In the thin-lens equation, f is negative for a convex mirror. Note that all mirrors, concave and convex, have only a single focal point.
what is the near point
The near point (NP) is the closest point on which the eye can focus with the ciliary muscles fully contracted. Objects closer than the NP cannot be brought to sharp focus.
what is the opticall axis
The optical axis is the line through the object and perpendicular to the boundary. The distance l is common to both the incident and refracted rays: 𝑙=𝑠tan𝜃_1=𝑠′tan𝜃_2
what is the path length difference
The path-length difference is just the short side of the triangle shown on the right: ∆r = d sin θ
what is a proton
The positive charge of the nucleus is associated with a positive subatomic particle called the proton (p). The proton's charge is equal but opposite in sign to the electron's charge. A proton is about 1800 times more massive than an electron. Electrons are more easily transferred than protons because protons are tightly bound in the nucleus.
Because of the wave nature of matter, a confined particle can only have certain energies.
The quantization of energy is the result that a confined particle can have only discrete values of energy. The number n is the quantum number, and each value of n characterizes one energy level of the particle in the box. The allowed energies are inversely proportional to both m and L2. Both m and L must be exceedingly small before energy quantization has any significance.
what does the retina do
The retina is the light-sensitive surface on which the image is formed, like the CCD of the camera.
what is the index of refraction
The speed of light in a material is characterized by the n=c/v
Virtual Images
The three refracted rays do not converge. The rays appear to diverge from point P¢. Point P¢ is a virtual image of the object point P. It is an upright image.
what are the two possible spin quantum numbers
The two possible spin quantum numbers, ms = ± ½ means that the electrons' intrinsic magnetic dipole points in the +z-direction or the -z-direction. The orientations are called spin up and spin down. It is convenient to picture a little vector that can be drawn for a spin-up state and ¯ for a spin-down state.
what is the wave model of light
The wave model of light is the most widely applicable model, responsible for the widely known "fact" that light is a wave. • As we have seen, in terms of classical physics, light essentially "is" a wave made of electric and magnetic fields. • It is certainly true that, under many circumstances, light exhibits the same behavior as sound or water waves. • Lasers and electro-optical devices, critical technologies of the 21st century, are best understood in terms of the wave model of light.
how is the wavelength in transparent material
The wavelength in the transparent material is shorter than the wavelength in a vacuum
what are isotopes
There is a range of neutron numbers that can form a nucleus with Z protons. Such a series of nuclei are called isotopes. The notation for isotopes is AZ, where A is the mass number.
when is there no phase change
There is no phase change at a boundary where the index of refraction decreases. so if n1 is greater than n2
what is the thin film interference
Thin-film interference is the interference of light waves reflected from two boundaries of a thin film. Thin-films are used for antireflection coatings on camera lenses, microscopes, and other optical equipment. The bright colors of oil slicks and soap bubbles are also due to thin-film interference.
what is angular size -
This is because the object makes a larger image on the retina and our brains interpret a larger image on the retina as representing a larger-appearing object.
why does an An object looks bigger when it is closer
This is because the object makes a larger image on the retina and our brains interpret a larger image on the retina as representing a larger-appearing object. -as the objects gets closer, the angle subtends to become larger, its angular size increases -the size of the image on the retina gets larger so the object's apparent size has increased
what is an extended source
This is the most common light source. The entire surface of an extended source is luminous, so that every point of an extended source acts as a point source. Lightbulbs, flames, and the sun are extended sources.
The discovery of large-angle scattering of alpha particles led Rutherford to envision an atom in which negative electrons orbit a small, massive, positive nucleus.
This is the nuclear model of the atom. Most of the atom is empty space.
what occurs witha concave mirror
This mirror is a concave mirror. Parallel waves reflect off the mirror and pass through the focal point.
what occurs in a concex mirror
This mirror is a convex mirror. The parallel rays that reflect off its surface appear to have come from a point behind the mirror.
what is a caemera
To record the image, digital cameras use a charge-coupled device or CCD. A CCD consists of an array of millions of detectors called pixels. When light hits a pixel, it generates an electronic charge proportional to the light intensity An image is recorded on the CCD in terms of little packets of charge. A CCD "chip" has pixels covered by red, blue, and green filters, which only record the intensity of light with that color. Later, the microprocessor interpolates nearby colors to give each pixel an overall true color.
Image Formation by Refraction
To your eye, the rays appear to diverge not from the object at point P, but instead from point P¢. The ruler appears closer than it really is because of refraction of light at the boundary.
what does Vstop not depend on
Vstop doesn't depend on the intensity. More intense light just causes more current, but the current always ceases when ΔV = -Vstop
what is absorptio
We can also consider the opposite case The system can absorb a photon, and "jump up" to a higher energy level. The frequency of the absorbed photon is given by
***what is the image distance sign for a virtual image
We define the image distance s′ to be negative for a virtual image. This is a sign convention.
Snell's law shows:
When a ray is transmitted into a material with a higher index of refraction, it bends to make a smaller angle with the normal. When a ray is transmitted into a material with a lower index of refraction, it bends to make a larger angle with the normal.
what is true about ane elctron in a stationary state
Whenever an electron is a stationary state (i.e. a bound orbit), the kinetic energy must be smaller in magnitude than the potential energy, and hence the atom's total energy is negative. (when using the convention Uelec = 0 at r = ∞
what does diffraction depend on
Whether a wave spreads out (diffracts) or travels straight ahead with sharp shadows on either side depends on the size of the objects that the wave interacts with.
Waves reflecting from any particular plane travel an extra distance Δr = 2d cos θ before combining with the reflection from the other planes. If Δr is a whole number of wavelengths, then the waves will be in phase when they recombine. X rays will reflect from the crystal coherently when the angle of incidence θm satisfies the Bragg condition:
X-ray diffraction patterns can reveal details of the crystal that produced them. Complex crystals produce correspondingly complex patterns that can help reveal the structure of the crystals that produced them. X-ray diffraction is still used to decipher the three-dimensional structure of biological molecules such as proteins.
To correct myopia
a diverging lens is used to defocus the rays and slightly move the image point back to the retina. -a diverging lens forms an image at the eye's far point
what are the three special rays for concave mirror
a) a ray is parallel to the axis and reflects through near focal point 2) a ray passes through focal point and reflects back parallel to axis 3)a ray strikes the center of the lens and reflects at an equal angle on the opposite side of the axis
The general condition for complete destructive interference depends on
a, the width of the slit λ, the wavelength of the light and is given by p labels the dark fringes asinthehta=plam Note that p = 0 is specifically excluded because p = 0 gives θp = 0, which would be the central maximum. The equation above for p > 0 locates the minima.
what are Spherical mirrors
are curved mirrors and can be used to form images.
what are gamma rays
are high-energy photons.
If K < |U|, then the electron
can't escape ( E < 0 )
what is convergig lens
causes the rays to refract toward the optical axis. oval shaped
what does refract incoming light rays to produce an image.
cornea the aqueous humor, and the lens
what is d
d is the distance between neighboring slits
material particles should also have a wave-like nature. De Broglie determined that if a material particle of momentum p = mv has a wave-like nature, its wavelength must is given by
de Broglie wavelength.
what is the spacing between any two adjacent fringes
delta y=wavelength times L/D
Self-luminous objects (or sources) Reflective objects
directly create light rays. Self-luminous objects include lightbulbs and the sun. are objects that reflect rays originating from self-luminous objects. These objects include a piece of paper or a tree.
what is a diverging lens
diverging lens causes the rays to refract away from the axis. thinner in teh center
If K > |U|, then the electro
electron can escape ( E > 0 )
If a system jumps from an initial state with energy Ei to a final state with lower energy Ef,
energy will be conserved if the system emits a photon with Ephoton = ΔEsystem.
what is the threshold frequency There is a threshold frequency for the ejection of electrons
f0=Eo/h
The photon must have a frequency corresponding to
fphoton=deltE/h -These photons form the emission spectrum of the quantum system. -Similarly, a photon will not be absorbed unless it has the exact frequency required for the system to jump to a higher-energy state.
For a person with hyperopia,
his or her eye needs assistance to focus the rays from a nearby object onto a closer-than-normal retina. The assistance is obtained by adding refractive power with a positive (converging) lens.
when does light undergo a phase change
if it reflects from a boundary at which the index of refraction increases. so if n1 is less than n2
For a particle such as an electron,
if you know where it is, you cannot know exactly how fast it is moving
What is presbyopia?
is the loss of accommodation, which arises because the lens loses flexibility. Presbyopia is known as a refractive error in the eye. Other refractive errors include hyperopia and myopia. All three can be corrected with lenses.
What is diffuse reflection?
is the process of reflecting incident light in all directions.
what is an object
it is a source of light rays, rays orginate from every point on the object and each point sends rays in all directions
Since the difference of paths is in the thin film, we need to use the wavelength of light there
lam'=lam/n
A light ray is a line in the direction along which energy of light is flowing.
light rays travel in straight lines light rays can cross
what is snell's law
n1sintheta=n2sintheta The index of refraction determines how much a light ray is bent when crossing the boundary between two different media (a consequence of the change in the speed of light as it crosses a boundary.)
what si the atomic number
of an element indicates its position in the periodic table It also represents the number of orbiting electrons in a neutral atom Thus it also represents the number of units of positive charge in the nucleus. The atomic number is represented by Z.
for converging lens
ray 1) a ray that goes from tip of object to parallel and goes through far focal point ray 2) passes through near focal point and emerges parallel ray 3) the ray goes through center of lens and straight through
what re alpha rays
rays (α), now called Alpha particles, are actually helium nuclei, with mass m = 6.64 × 10-27 kg, emitted at high speed from a sample.
what is the image distance equation as
s'=𝑛_2/𝑛_1 𝑠
what is thetac critical angle
sin-1(n2/n1)
what is single silt diffraction
single s diffraction is diffraction through a tall, narrow slit of width a. -The light pattern on the viewing screen consists of a central maximum and a series of weaker secondary maxima and dark fringes. -The central maximum is much broader and brighter than the secondary maxima.
If ΔV is ~ +1 V or more,
the current barely changes as ΔV is increased
directions for ray tracing with converging lens
the focal length is always postivie 1) a ray that starts parallel and then passes through lens to go through far focal point 2) a ray that enters lens along a through the near focal point and goes straight through parallel 3) ray that goes throgh center of lens and does not bend
what does m describe
the orientation of the image relative to the object and its size
how does the light overlap
the two waves overlap as they spread out behind the two slits. the two overlapped waves interfere resulting in a pattern of light and dark bands on the screen
The angular size of the object, if located very close to the focal point f of the magnifier is
theta=h/f
If the waves are in phase If they are out of phase
they will interfere constructively and cause a strong reflection. they will interfere destructively and cause a weak reflection, or no reflection at all. The path-length difference of the reflected waves is Δr = 2t because the second wave travels through the film of thickness t twice.
Destructive interference occurs when the difference Δr differs by a whole number of wavelengths plus a half:
|Δ𝑟|=(𝑚+1/2)𝜆,
Constructive interference occurs at a point where the distances r1 and r2 from the slits differ by a whole number of wavelengths
|Δ𝑟|=𝑚𝜆,
what is the photon model of light
• Modern technology is increasingly reliant on quantum physics. • In the quantum world, light consists of photons that have both wave-like and particle-like properties. • Photons are the quanta of light.
The work function energy E0 is the minimum energy needed to remove an electron, so the maximum possible kinetic energy of an ejected electron is
𝐾_𝑚𝑎𝑥=ℎ𝑓−𝐸_0
Combining Kmax = hf - E0 with the previous expression for Kmax, Kmax = eVstop, we get
𝑒𝑉_stop=𝐾_max=ℎ𝑓−𝐸_0
