Physics 2: Exam 2
radio wave magnetic field can be detected by loop
(normal is parallel with magnetic field B)
on test, he will have like 5 polarizers at same angle (can set equation to exponent of however many polarizers)
* (cos@)^2 for each additional polarizer
object is always at a ___ distance from lens/mirror
+ d(object)
image distance (lenses)
+ for real images (opposite of object/observer) - for virtual images (same side as object/observer)
other weird concave placements
- between F and mirror = bigger and upright - on focal point = no image - between C and F = inverted, larger - on C (center of curvature) = inverted same size image at same place as image - L of C = smaller, inverted image is where 2 reflected light guys converge
A candle is placed 13.28 cm in front of a convex mirror. When the convex mirror is replaced with a plane mirror, the image moves 7.0 cm farther away from the mirror. Find the focal length of the convex mirror.
-11.914cm
When someone looks into a concave mirror from a distance of 25 cm, a virtual image is produced that is enlarged by a factor of 2. What is the image distance?
-50 cm The image distance is di = -mdo = -2(25 cm) = -50 cm
speed of light
3.00 x 10^8 m/s speed of electromagnetic wave in a vacuum
An electromagnetic wave in a vacuum has a magnetic field with a magnitude of 1.14 × 10-6 T. What is the intensity S / I of the wave?
310.26 J/sm^2 equation on sheet only works without 2
Light rays that are near and parallel to the principal axis of a concave mirror converge to a point 18 cm in front of the mirror. What is the radius of curvature of the mirror?
36 cm Parallel rays that are near the principal axis converge at the focal point after reflecting from a concave mirror. The radius of curvature is twice the focal length (see Equation 25.1), so R = 2f = 36 cm.
ex: f = 6, do = 3 convex mirror
6 becomes -6 because convex mirror di = -2 (virtual) m = +2/3 (smaller, right-side up)
The drawing shows a top view of an object to the right of a plane mirror. An observer looks into the mirror. At what location, A, B, C, or D, does the observer see the image?
A The image is as far behind the mirror as the object is in front of the mirror. In addition, the image and the object lie on the horizontal line that is perpendicular to the mirror.
radio wave
Electromagnetic waves with the longest wavelengths and lowest frequencies (lowest energy) - can be detected with a receiving antenna wire that is parallel to the electric field
unpolarized strikes polarizer
I = 1/2 I0 true for any angle of polarizer usually in W/m^2
polarized strikes polarizer
I = I0 cos^2@ Malus's Law @ = angle between direction of polarization of incident light and transmission axis either when unpolarized goes through 2nd filter, or when polarized goes through 1st filter
polarized vs. unpolarized light
In polarized light, the electric field fluctuates along a single direction. Polarized light may be produced from unpolarized light with the aid of polarizing material.
The drawing shows two sheets of polarizing material, which have their transmission axes crossed. The sheet on the left has its transmission axis aligned vertically. Light is incident from the left, as shown and can be either completely unpolarized or completely polarized along the vertical direction. Which one of the following statements is true concerning the light that exits the polarizer on the right?
No light exits the polarizer on the right for either the unpolarized or the polarized incident light. When the unpolarized light strikes the first polarizer, the light that passes through it is polarized in the vertical direction. When this polarized light strikes the second polarizer, all of it is absorbed, since the two polarizers are crossed. When the polarized light strikes the first polarizer, all of it passes through, since the direction of polarization and the transmission axis are both vertical. When this polarized light strikes the second polarizer, all of it is absorbed, since the two polarizers are crossed. Thus, no light exits the polarizer on the right in either case
on final exam: lens + mirror do(1) = 15 cm find final dimg and M Given
Pink WEEK 8 P9
~ doppler effect (not class)~
Sound waves require a medium, whereas electromagnetic waves do not. For sound, it is the motion relative to the medium that is important. For electromagnetic waves, only the relative motion of the source and observer is important
diffraction
The bending of a wave as it moves around an obstacle or passes through a narrow opening
~~ The indices of refraction for red, green, and violet light in glass are nred = 1.520, ngreen = 1.526, and nviolet = 1.538. When a ray of light passes through a transparent slab of glass, the emergent ray is parallel to the incident ray, but can be displaced relative to it unless the angle of incidence is zero. For light passing through a glass slab that is surrounded by air, which color is displaced the most?
Violet The displacement occurs because of the refraction or bending of the ray that occurs when the ray enters and leaves the glass. The bending is greater when the refractive index is greater. Hence, the displacement is greatest for violet light.
Suppose you hold up a small convex mirror in front of your face. Which answer describes the image of your face?
Virtual, upright A convex mirror always produces a virtual, upright image
on exam exactly: 2 lens f1 = 20cm f2 = 10cm do(1) = 22cm do(2) = 9cm Find di(1), di(2)
WEEK 8 PG7
Which of the following is/are true? a. Electromagnetic waves are created by accelerating charges. b. Electromagnetic waves are transverse waves. c. Electromagnetic waves consist of time-varying electric and magnetic fields that are mutually perpendicular. d. Electromagnetic waves move at the speed of light in a vacuum. e. All of the above are true.
e. All of the above are true.
Two straight wires connected to the terminals of an AC generator can create an
electromagnetic wave - Only the electric wave traveling to the right is shown here.
True or False: The speed of light in a vacuum depends only on the electric permittivity of free space.
false
~ (no class, eq not on sheet) Intelligent beings in a distant galaxy send a signal to earth in the form of an electromagnetic wave. The frequency of the signal observed on earth is 2.0% greater than the frequency emitted by the source in the distant galaxy. What is the speed vrel of the galaxy relative to the earth?
fobserved =((c+v)/c)factual 1.02 = (c+v)/c 0.02c = v v = (0.02)*(3E10^8) =6,000,000 m/sec
moving closer
higher frequency, smaller wavelength bluer
The drawings show two examples in which a ray of light is refracted at the interface between two liquids. In each example the incident ray is in liquid A and strikes the interface at the same angle of incidence. In one case the ray is refracted into liquid B, and in the other it is refracted into liquid C. The dashed lines denote the normals to the interfaces. Rank the indices of refraction of the three liquids in descending order (largest first).
if light is bent away from the normal when travelling from one material to another, then the first material had a greater index of refraction (n1>n2) When the light is refracted into liquid B it is bent away from the normal, so that nA > nB. When the light is refracted into liquid C it is bent toward the normal, so that nC > nA. Therefore, we conclude that nC > nA > nB
planar mirror
image is always inside mirror distance from mirror to inside is same as from mirror to object, in opposite directions
~at polarizing angle, reflected and refracted angles are at 90 degrees from one another
in this picture, because N is 180, @P + @r = 90 reflected angle is completely polarized, but refracted rate is only partially polarized
law of reflection
incident angle is = reflected angle
on exam: How can you create a virtual image with a concave mirror?
inside focal length = giant version of object look up A virtual image is produced by a concave mirror when the object is placed inside the focal length of the mirror. The image is located behind the mirror so you cannot touch it (that is why it is called virtual). It is easy to recognize virtual images with your eyes because they are upright. A real image occurs when an object is placed outside the focal length of the concave mirror. The image is located in front of the mirror so you can touch it (that is why it is called real). It is easy to recognize real images because they are upside down.
relationship between wavelength and frequency
inverse
converging lens picture
inverted when hi is - upright when hi is + virtual when -di (on left) real when +di (on right) (what youre actually looking at through lens)
A wave front __________
is a surface on which all points of the wave are in the same phase of motion
how does the critical angle for total internal reflection change when the ratio between indices of refraction n2/n1 of the two media decreases?
it gets smaller relative to the normal as n2/n1 decreases, sin@c also decrease, so @c decreases
~ why do most telescopes use mirrors and not lenses?
lenses have chromatic aberration, but mirrors do not
90 degrees will be 0
light that passes through filter will always have same direction as filter
moving away
lower frequency, higher wavelength redder
diverging lens example f=4 do=12
make f - because diverging lens di = -3 (negative, so virtual image, on left side) m = 1/4 (upright, smaller)
If light travels from high n to low n
n is decreasing (going from higher to lower), greater angle of refraction (compared to incident angle) : - angle moves away from normal - has internal reflection
If light travels from low n to high n
n is increasing (going from lower to higher), lower angle of refraction (compared to incident angle) : - angle moves towards the normal - has no internal reflection
~~ A coin is resting on the bottom of an empty container. The container is then filled to the brim three times, each time with a different liquid. An observer (in air) is directly above the coin and looks down at it. With liquid A in the container, the apparent depth of the coin is 7 cm, with liquid B it is 6 cm, and with liquid C it is 5 cm. Rank the indices of refraction of the liquids in descending order (largest first).
nC, nB, nA apparent depth and the refractive index are inversely proportional
polarization by reflection
no polarization if 0 degrees with normal partial polarization at most other incident angles complete polarization if at Brewster's angle, where reflected R and refracted r rays are at right angles
incidence is polarized
plates are 42 relative to each other, incoming is 21 from each I does not = 1/2 I0
part b 65
polarized incident light = max - min
Brewster's angle (was just a plug in class)
polarizing angle; the angle at which reflected light will be completely polarized parallel to the surface of the interface. @B = tan^(-1) [n2/n1] at polarizing angle, reflected and refracted angles are at 90 degrees from one another
An electromagnetic wave is traveling in a vacuum. The magnitudes of the electric and magnetic fields of the wave are _____________, and the electric and magnetic energies carried by the wave are _____________.
proportional (but not equal) to each other, equal The magnitudes of the electric and magnetic fields of the wave are proportional to each other, according to E = cB a wave carries equal amounts of electric and magnetic energy.
total light =
refracted (into material) + reflected
intensity
the amount of energy in a light or sound wave, which we perceive as brightness or loudness, as determined by the wave's amplitude
polarizing angle ~
the angle at which reflected light will be completely polarized parallel to the surface of the interface.
law of reflection
the angle of incidence is equal to the angle of reflection
focal length
the distance from a lens to its focus F = R/2 where R is radius of circle if mirror was a whole circle change to : + for concave - for convex the distance from the mirror at which rays coming from a very distanced light source (infinite object distance) will be focused. For some systems such as a convex mirror, since the rays from a distant object will actually be divergent, the focal point is virtual, as it is behind the mirror and the rays only appear to be focused. The focal distance f is an important characteristic of an optical element. It is used to analytically calculate the position of the images.
electromagnetic spectrum
the range of wavelengths or frequencies over which electromagnetic radiation extends. electromagnetic waves : transverse waves consisting of changing electric fields and changing magnetic fields; carry energy
Magnification
the ratio of an object's image size to its real size - means image is inverted + means image is upright (not sure about these) |M| = 1 means image is same size |M| > 1 means image is bigger |M| < 1 means image is smaller
critical angle
total internal reflection when angle of refraction = 90 degrees, the angle of incidence becomes the critical angle ex: n(glass) = 1.5 n(air) = 1 - put bigger angle on bottom @c = sin^(-1) [1/1.5] = 41.81 degrees
electromagnetic waves
transverse waves consisting of changing electric fields and changing magnetic fields
part a 65
unpolarized incident light = minimum intensity
electromagnetic spectrum
wavelength increases to L energy/frequency increases to R increased wavelength = decreased frequency/energy
polarization of light (in class)
whenever light is coming off a light source, 1/2 intensity after going through polarizer I = 1/2 I0 (vertically polarized, usually first one) I = I0cos^2@ (at an angle) (book uses S instead of I) ~
adding third filter increased final intensity
would have just been 0 bc 90 degrees
What kind of image can a single converging lens not produce? A real image that is inverted and is larger with respect to the object. A virtual image that is upright and smaller with respect to the object. A virtual image that is upright and is larger with respect to the object. A real image that is inverted and is smaller with respect to the object.
A virtual image that is upright and smaller with respect to the object A converging lens can produce an upright virtual image, if the object is within the focal point of the lens. However, this image is larger (not smaller) than the object
AM vs FM waves
AM are longer wavelength, reflect off ionosphere, prone to interference by weather and atmosphere - amplitude varies FM have less range - frequency varies - easily blocked by building or mountain - "line of sight"
real image
An upside-down image formed where rays of light meet.; flipped + distance (in front of mirror), magnification - light rays converge can be projected onto wall or something; rays of light from object converge
The figure at the right shows three situations - A, B, and C - in which an observer and a source of electromagnetic waves are moving along the same line. In each case the source emits a wave of the same frequency. The arrows in each situation denote velocity vectors relative to the ground and have magnitudes of either v or 2v. Rank the magnitudes of the frequencies of the observed waves in descending order (largest first).
BAC
Consider two electromagnetic waves A and B traveling in vacuum, where the frequency of A is twice that of B (fA=2fB). Which of the following is/are true?
The speed of wave A is equal to the speed of wave B. (ew travel at c in vacuum)
The drawing shows an x, y, z coordinate system. A circular loop of wire lies in the z, x plane and, when used with an LC tuned circuit, detects an electromagnetic wave. Which of the following situations would result in the detection of an electromagnetic wave?
The wave travels along the z axis, and its electric field oscillates along the x axis. The loop can only detect the wave if the wave's magnetic field has a component perpendicular to the plane of the loop (parallel to normal), that is, along the y axis. Only then will there be a changing magnetic flux through the loop. The changing flux is needed, so that an induced emf will arise in the loop according to Faraday's law of electromagnetic induction. The electric and magnetic fields of an electromagnetic wave are mutually perpendicular and are both perpendicular to the direction in which the wave travels. Thus, when the wave travels along the z axis with its electric field along the x axis, the magnetic field will be along the y axis as needed. Explanation The wave can be detected when the magnetic field oscillates perpendicular to the circular loop. Thus from the figure the magnetic field is along the y-axis. The loop is in zx-plane the electric field is perpendicular to the magnetic field and hence the electric field is along the x-axis. The electromagnetic wave propagates perpendicular to both electric and magnetic fields. hence the wave propagates along Z-axis.
virtual, real, upright, inverted
UV - Upright Virtual For lenses, a virtual image is on the same side as the object. For mirrors, a virtual image is opposite the object. (-d) IR - Inverted Real For lenses, a real image is on the opposite side of the object. For mirrors, same side. (+d)
convex mirror
a mirror that curves outward - reflect light outward - creates image in mirror that is smaller and upright - virtual image negative - focal length (f) (into mirror) - radius of curvature is - for all length - - do does not exist
virtual image
a reflected optical image (as seen in a plane mirror) right side up - distance (inside mirror), magnification - light rays dont actually converge (diverge at surface of mirror) - plane mirror is always virtual
electromagnetic wave
a wave that consists of oscillating electric and magnetic fields, which radiate outward at the speed of light
second filter is one angle, third filter is another
angle in equation for intensity after 3rd = difference between 2 angles last ans is 1/8I
TIR (total internal reflection) occurs when
angle of incidence > critical angle - no more refraction - because angle of refraction can't be more than 90, all there can be is reflection
reduction in intensity that takes place
assume initial intensity is 1
An astronomer observes that the wavelength of light from a distant star is shifted toward the red part of the visible spectrum. Which of the following is true? a. The distance between the earth and the star is decreasing. b. The distance between the earth and the star is increasing. c. The distance between the earth and the star is remaining constant.
b
Consider two electromagnetic waves A and B traveling in vacuum, where the frequency of A is twice that of B (fA=2fB). Which of the following is/are true? a. The speed of wave A is ½ the speed of wave B. b. The speed of wave A is equal to the speed of wave B. c. The wavelength of wave A equals the wavelength of wave B. d. The wavelength of wave A is twice the wavelength of wave B.e. The speed of wave A is twice the speed of wave B.
b
concave mirror
cave - reflect light inward (using it to focus light can be used to generate heat) Outside of Focal Point: - can be used to project a bigger and upside-down image - real image (+di) Inside of Focal Point: - can be used to project a bigger and upright image - virtual image v(-di) positive + focal length (f)
diverging lens
concave lens - focal length is - (opposite of concave mirror) - always virtual, smaller, and upright same equations - focal point of lens is before retina
converging lens
convex lens - focal length is + (opposite of convex mirror) - real, inverted (when outside focal point) - virtual, upright, enlarged (when between focal point and lens) same equations - used when focal point of lens is behind retina - wont work on focal point - image smaller than object when outside of 2f
90 degree angle of refraction
critical angle = incident angle
ex: f = 8, do = 14, ho = 4 concave mirror find hi, di, M, whether image is real or virtual, upright or inverted, bigger or smaller
di = 12 (positive, so real) m = -0.5 (negative, so inverted; <1, so smaller) hi = -2
converging lens example f=6 do =8 h0 = 2
di = 24 (positive, so real image, on right side) m = -3 (inverted, enlarged) ~ hi = -6 (inverted because negative) ~
d(image)
distance between image and mirror - use to determine virtual or real Mirrors: + if image is in front of mirror, real - if image is behind mirror, virtual
