Deck 11: Properties of Light

Question 1

Use the following figure for the next two problems.
An object leaves point A and travels in a straight line to point B via path b. In region I, the speed is 100 m/s while in region II, the speed is 71 m/s. How long does it take for the object to go from A to B?

A) 82.0 ms
B) 70.8 ms
C) 61.3 ms
D) 34.3 ms
E) 27.7 ms

Answer 1

61.3 ms

Question 2

As light passes from one medium into another, the angle of refraction is _____ in the medium with the _____ index of refraction and _____ speed of light.

A) smaller; larger; lower
B) smaller; larger; higher
C) larger; smaller; lower
D) larger; larger; lower
E) smaller; smaller; higher

Answer 2

smaller; larger; lower

Question 3

You see a fish in water at an apparent depth of 1.83 m. The actual depth of the fish, if the index of refraction of the water relative to air is 4/3, must be

A) 3.81 cm
B) 61.0 cm
C) 1.37 m
D) 1.83 m
E) 2.44 m

Answer 3

2.44 m

Question 4

Which of the following statements is true about the speeds of the various colors of light in glass?

A) All colors of light have the same speed in glass.
B) violet has the highest speed, red the lowest
C) red has the highest speed, violet the lowest
D) green has the highest speed, red and violet the lowest
E) red and violet have the highest speed, green the lowest

Question 5

Light is incident on a piece of glass in air at an angle of 37.0º from the normal. If the index of refraction of the glass is 1.50, the angle that the refracted ray makes with the normal is approximately

A) 8.6º
B) 21.8º
C) 23.6º
D) 41.8º
E) 56.4º

Question 6

A ray of light strikes a slab of glass at an angle of incidence of 35º. The angle of refraction in the glass is

A) 22º
B) 63º
C) 27º
D) 90º
E) None of these is correct.

Question 7

Ultra fast pulse lasers can emit pulses of the order 10 fs. The length of each pulse that is 10 fs long is

A) 1.0 $\mu$ m
B) 2.0 $\mu$ m
C) 3.0 $\mu$ m
D) 9.0 $\mu$ m
E) 12.0 $\mu$ m

Question 8

A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45º. Which of the following four quantities change as the light enters the water: (1) wavelength, (2) frequency, (3) speed of propagation, and (4) direction of propagation?

A) 1 and 2 only
B) 2, 3, and 4 only
C) 1, 3, and 4 only
D) 3 and 4 only
E) 1, 2, 3, and 4

Question 9

Mission Control sends a brief wake-up call to astronauts in a distant spaceship. Five seconds after the call is sent, Mission Control hears the waking groans of the astronauts. How far away (at most) from Earth is the spaceship?

A) 7.5 * 10⁸ m
B) 15 *10⁸ m
C) 30 * 10⁸ m
D) 45 * 10⁸ m
E) The spaceship is on the moon.

Question 10

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is

A) very much greater.
B) a little greater.
C) the same.
D) a little less.
E) very much less.

Question 11

A light wave traveling at speed v₁ in medium 1 passes into medium 2 where its speed is v₂. By which of the following equations is the frequency f₁ of the wave in medium 1 related to its frequency f₂ in medium 2? ( $\theta$ ₁ and $\theta$ ₂ are the angles of incidence and refraction.)

A) f₁ sin $\theta$ ₁ = f₂ sin $\theta$ ₂
B) f₁v₂ = f₂v₁
C) f₁ = f₂
D) f₁v₁ = f₂v₂
E) f₁ sin $\theta$ ₂ = f₂ sin $\theta$ ₁

Question 12

Light that has been traveling in a medium with an index of refraction n₂ is incident on the boundary surface of another medium with an index of refraction n₁. Given a sufficient angle of incidence, which of the following conditions must be satisfied for total internal reflection to occur?

A) n₁ < n₂
B) n₁ > n₂
C) n₁ = n₂
D) Any of these may be correct.
E) None of these is correct.

Question 13

From directly above, you're watching a fish swim 1.83 m beneath the surface of a clear lake (n = 1.33). How far beneath the surface does the fish seem to be?

A) 0.914 m
B) 1.37 m
C) 1.83 m
D) 2.44 m
E) 2.93 m

Question 14

A glass block with index of refraction 1.50 is immersed in water whose index of refraction is 1.33. The critical angle at the glass-water interface is

A) 6.5º
B) 41.9º
C) 48.8º
D) 56.3º
E) 62.5º

Question 15

Ultra fast pulse lasers can emit pulses of the order 10 fs. If each pulse that is 10 fs long and the wavelength of the laser is 500 nm, the number of wavelengths in each pulse is

A) 6
B) 10
C) 12
D) 50
E) 120

Question 16

Communications satellites are usually placed in geosynchronous orbits, a distance of 4.43 * 10⁷ m from the center of Earth. What is the time lag for a signal sent from one point on Earth's surface to another via such a satellite? (The radius of Earth R_E = 6.370 *10⁶ m.)

A) 0.13 s
B) 0.25 s
C) 0.51 s
D) 0.29 s
E) 0.15 s

Question 17

Light traveling in a transparent medium with an index of refraction n₁ is incident on a transparent boundary with a second transparent medium with an index n₂. Very little light is transmitted into the second medium. Which of the following statements must be true?

A) n₁ equals n₂
B) n₁ is somewhat greater than n₂
C) n₂ is somewhat greater than n₁
D) n₂ is much greater than n₁
E) Either index of refraction is much greater than the other

Question 18

You are trying to catch fish by using a spear. You observe a large fish a couple of meters in front of you and a meter below the water surface. In order to hit the fish with your spear you must aim (assume that the fish is stationary and does not swim away in fright)

A) directly at the point where you see the fish.
B) slightly above the point where you see the fish.
C) slightly below the point where you see the fish.
D) slightly to the left side of the point where you see the fish.
E) slightly to the right side of the point where you see the fish.

Question 19

It has been suggested that a fundamental physical unit of time is the time required for light to traverse the diameter of the nucleus of an atom (approximately 3 *10^-13 m). This unit of time is approximately

A) 1 s
B) 10^-4 s
C) 2 * 10^-20 s
D) 10^-21 s
E) 10^-23 s

Question 20

Use the following figure for the next two problems.
An object leaves point A and travels to point B via path a. In region I, the speed is
100 m/s while in region II, the speed is 71 m/s. How long does it take for the object to go from A to B?

A) 80.0 ms
B) 60.8 ms
C) 40.6 ms
D) 32.4 ms
E) 26.8 ms

Question 21

A light ray makes an angle of 42º with the normal to a glass-water surface on the glass side of the surface. The angle $\theta$ in the water is

A) 42º
B) 36º
C) 63º
D) 49º
E) 27º

Question 22

The prism totally reflects some wavelengths of light as shown, but other wavelengths pass through. The index of refraction of this prism for the longest wavelengths that are totally reflected is approximately

A) 1.50
B) 1.53
C) 1.46
D) 1.41
E) 1.59

Question 23

A ray of light strikes a water-glass interface at an angle of incidence of 35º. The angle of refraction is

A) 40.3º
B) 22.1º
C) 30.6º
D) 59.4º
E) 19.7º

Question 24

Monochromatic light is incident on the prism at the proper angle for minimum deviation. The emergent ray passes through which point?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 25

The light ray that passes through the prism and emerges at the angle of minimum deviation for that ray is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 26

In the laboratory you used the spectrometer to determine the indices of refraction of various wavelengths of light. The curve that could represent a plot of the index of refraction as a function of the wavelength of the light is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 27

Light travels in a medium of index of refraction n', passes into a medium of index n", where n" > n', and then into air, where n_air < n' < n". The ray that correctly shows the light path is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 28

A ray of light traveling in air enters the end of a rectangular block of a material that has an idex of refraction n = 1.35. The largest value of the angle $\theta$ for which total internal reflection occurs at the upper surface of the material is approximately

A) 75º
B) 48º
C) 56º
D) 78º
E) None of these is correct.

Question 29

For the prism immersed in water (n = 1.33), the minimum index of refraction that will produce total reflection of the indicated ray is approximately

A) 0.94
B) 1.28
C) 1.50
D) 1.65
E) 1.88

Question 30

The light ray that passes through the prism and emerges at the angle of minimum deviation for that color is

A) red
B) yellow
C) green
D) blue
E) violet

Question 31

When a ray of light traveling in air is incident at $\theta$ = 50º on a plane-parallel slab of glass as illustrated, the light ray

A) is 100 percent reflected at the first surface.
B) is 100 percent reflected at the second surface.
C) emerges parallel to the incident ray and is not displaced to one side or the other of the incident ray.
D) is absorbed if the wavelength is greater than 450 nm.
E) is not described by any of these statements.

Question 32

The light ray in the figure is incident on a glass-air surface. The index of refraction of the glass is 1.74. The approximate critical angle for total internal reflection is

A) 48º
B) 35º
C) 30º
D) 22º
E) None of these is correct.

Question 33

You shine light of frequency 4.00* 10¹⁴ Hz through a glass plate whose index of refraction for this light is 1.50. The wavelength of this light in the glass is approximately

A) 500 nm
B) 110 nm
C) 800 nm
D) 425 nm
E) 380 nm

Question 34

The speed of yellow sodium light in a certain liquid is 1.92 * 10⁸ m/s. With respect to air, the index of refraction of this liquid for sodium light is approximately

A) 1.92
B) 1.56
C) 1.23
D) 0.64
E) 1.33

Question 35

The diagram shows a ray of light entering a block of polyethylene (n = 1.5). The path of this ray after it has passed through the block is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 36

A light ray traveling in glass strikes a glass-water surface. At angles greater than $\theta$ _c the light ray is totally internally reflected. The value of $\theta$ _c is

A) 15º
B) 31º
C) 45º
D) 23º
E) None of these is correct.

Question 37

Light from an underwater source at O impinges upon a water-air interface. The critical angle is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 38

A small beam of monochromatic light in air is incident on a large plate of glass with plane-parallel sides at an angle of 30º. The index of refraction of the glass plate for this wavelength is 1.50. The angle of emergence of the light on the far side of the plate is approximately

A) 30º
B) 45º
C) 20º
D) the angle whose sine is 1/3.
E) 60º

Question 39

An air prism is immersed in water. A ray of monochromatic light strikes one face as shown. The emerging ray is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 40

A ray of monochromatic light in air falls on the upper surface of two parallel-sided slabs of transparent material, as shown in the diagram. The angle of refraction $\phi$ in the lower slab is approximately

A) 22º
B) 30º
C) 37º
D) 53º
E) 60º

Question 41

The figure shows the wavelength of light that is normally incident on and transmitted through a refractive medium. The index of refraction of this medium is

A) 1.0
B) 1.5
C) 2.0
D) 0.67
E) 3.0

Question 42

A ray of light is shown reflected and refracted at the surface of a liquid. From the diagram you can determine that the speed of light in this liquid is approximately

A) 1.83 * 10⁸ m/s
B) 2.24 * 10⁸ m/s
C) 3.00 *10⁸ m/s
D) 4.02 * 10⁸ m/s
E) 2.50 *10⁸ m/s

Question 43

A 6 $\degree$ prism has a refractive index of 1.52. Calculate the angle of incidence for the initial light ray that is then refracted inside the prism and just undergoes total internal reflection at the opposite face of the prism.

A) 41.1 $\degree$
B) 18.9 $\degree$
C) 29.4 $\degree$
D) 30.6 $\degree$
E) 60.6 $\degree$

Question 44

A column of liquid is 10 cm high. Viewed from above the liquid has an apparent depth of 6.77 cm. If the refractive index of the liquid is 1.33 at the top and increases uniformly to the bottom, then what is the refractive index at the bottom of the liquid?

A) 1.96
B) 2.95
C) 1.48
D) 1.62
E) None of these is correct.

Question 45

Use the following figure below for the next three problems The figure shows a cross-section of a fiber optic.

-A fiber optic is made by cladding a thin fiber core of refractive index n₁ = 1.45 with a material of refractive index n₂ = 1.38. The numerical aperture of a fiber optic is defined as NA = n_air sin $\theta$ _m, where $\theta$ _m is the maximum incident angle so that the light ray is totally internally reflected inside the fiber. The NA for the fiber is

A) 0.445
B) 0.614
C) 0.645
D) 0.407
E) 0.470

Question 46

An "X" is marked on the bottom of a glass container. A microscope is adjusted so that it is focused on the "X." A liquid is now poured into the glass to a depth of 6.00 cm. If the microscope has to be backed up by a distance of 1.50 cm to refocus on the "X," then calculate the refractive index of the liquid.

A) 1.25
B) 4.00
C) 1.33
D) 0.75
E) 3.00

Question 47

Use the following figure below for the next three problems The figure shows a cross-section of a fiber optic.

-A fiber optic is made by cladding a thin fiber core of refractive index n₁ = 1.45 with a material of refractive index n₂ = 1.38. What is the maximum incident angle, $\theta$ , so that the light ray is totally internally reflected inside the fiber?

A) 24.1º
B) 26.4º
C) 28.2º
D) 30.3º
E) 32.7º

Question 48

The index of refraction is related to the prism angle and the angle of minimum deviation by n = sin ½( $\delta$ + $\phi$ )/sin ½ $\phi$
The angle of minimum deviation in the figure is angle

A) 1
B) 2
C) 3
D) 4
E) 5

Question 49

The critical angle for light rays passing from flint glass (n = 1.70) into air is about

A) 3.4º
B) 36º
C) 44º
D) 54º
E) 90º

Question 50

A plane wavefront of light (AA') approaches an air-water interface as shown. n < n'. The refracted wave is best represented by

A) 1
B) 2
C) 3
D) 4
E) None of these is correct. There is no refraction because $\theta$ is less than the angle of total internal reflection.

Question 51

If the refractive index of glass is 1.5 and the refractive index of a particular liquid is 1.38, then calculate the value for the critical angle of total internal reflection at the liquid-glass interface.

A) 23.1 $\degree$
B) 66.9 $\degree$
C) 82.8 $\degree$
D) 42.6 $\degree$
E) None of these is correct.

Question 52

The minimum angle of deviation produced by a glass prism (n = 1.70 for the light used) whose apex angle is 45º is approximately

A) 32º
B) 36º
C) 26º
D) 18º
E) 45º

Question 53

A light wave in air strikes a glass plate 1 cm thick at an angle of incidence of 50.0º. If the index of refraction of the glass is 1.50 for this light, the actual path length of the light through the glass is approximately

A) 0.51 cm
B) 1.16 cm
C) 1.50 cm
D) 2.11 cm
E) 7.66 cm

Question 54

The rays in the figure are reflected and refracted at the front and back surfaces of the glass. Which of the following is true of these rays?

A) $\angle$ 1 = $\angle$ 2 = $\angle$ 3 = $\angle$ 4
B) $\angle$ 1 = $\angle$ 2; $\angle$ 3 = $\angle$ 4; but $\angle$ 1 $\neq$ $\angle$ 3
C) $\angle$ 1 = $\angle$ 2 = $\angle$ 3; but $\angle$ 4 $\neq$$\angle$ 1
D) $\angle$ 1 = $\angle$ 4; but $\angle$ 2 $\neq$ $\angle$ 4
E) $\angle$ 1 $\neq$ $\angle$ 2 $\neq$ $\angle$ 3 $\neq$$\angle$ 4

Question 55

The wavelength of green light in air is 500 nm. The wavelength of this light in glass of index of refraction 1.60 is approximately

A) 313 nm
B) 500 nm
C) 750 nm
D) 800 nm
E) 427 nm

Question 56

You place a point source of light at the bottom of a pool of water 1.00 m deep. The source emits rays upward in all directions. You notice that a circle of light is formed by the rays that are refracted into the air and that the rays outside of this circle are reflected back into the water. The index of refraction of water is 1.33. The radius R of the circle at the surface of the water is approximately

A) 0.75 m
B) 1.00 m
C) 1.13 m
D) 1.33 m
E) infinite

Question 57

A light wave traveling in air impinges on an amber plate at an angle of incidence of 60º. If the angle of refraction is 34º, the velocity of light in amber must be approximately

A) 0.52 * 10⁸ m/s
B) 4.64 *10⁸ m/s
C) 1.86 * 10³ m/s
D) 2.09 *10⁸ m/s
E) 4.64 * 10¹⁰ m/s

Question 58

Use the following figure below for the next three problems The figure shows a cross-section of a fiber optic.

-A fiber optic is made by cladding a thin fiber core of refractive index n₁ = 1.45 with a material of refractive index n₂ = 1.38. What is the critical angle, $\theta$ _c, at the core-cladding interface?

A) 44º
B) 46º
C) 55º
D) 72º
E) None of these is correct.

Question 59

Two clear but non-mixing liquids each of depth 15 cm are placed together in a glass container. The liquids have refractive indices of 1.75 and 1.33. What is the apparent depth of the combination when viewed from above?

A) 19.8 cm
B) 23.1 cm
C) 17.7 cm
D) 9.9 cm
E) None of these is correct.

Question 60

A ray of light in glass is incident on a glass-air interface as shown. You would expect the ray to pass through

A) point 1 only.
B) point 3 only.
C) point 4 only.
D) points 2 and 4.
E) points 1 and 4.

Question 61

A 60 $\degree$ prism has a refractive index of 1.71. Calculate the angle of emergence out of the prism for a ray that enters one side at an angle almost parallel to one face, i.e. at 90 $\degree$ to the normal.

A) 24.3 $\degree$
B) 35.8 $\degree$
C) 45.1 $\degree$
D) 48.7 $\degree$
E) 55.3 $\degree$

Question 62

One would not attempt to polarize light by

A) selective absorption.
B) reflection from a surface.
C) passage through a narrow slit.
D) scattering.
E) double refraction.

Question 63

Light is incident at an angle of 60 $\degree$ at an air to glass interface. If the angle of refraction inside the glass is 32 $\degree$ , then calculate the speed of light within the glass.

A) 3.00 * 10⁸ m/s
B) 1.77 * 10⁸ m/s
C) 4.90 * 10⁸ m/s
D) 1.84 * 10⁸ m/s
E) 1.62 * 10⁸ m/s

Question 64

Which of the following is not a phenomenon by which polarized light can be produced from unpolarized light?

A) absorption
B) reflection
C) birefringence
D) diffraction
E) scattering

Question 65

Light is reflected from the surface of a lake (n = 1.33). What is the angle of incidence for which the reflected light is 100 percent polarized?

A) 53º
B) 49º
C) 45º
D) 41º
E) 37º

Question 66

In any wave motion, dependence of velocity on wavelength is called

A) polarization
B) deviation
C) dispersion
D) diffraction
E) scattering

Question 67

If you look at a dot on a piece of paper through a calcite crystal lying on the paper, you will see two images of the dot, one of which appears to be nearer to you than the other. From this evidence you can conclude that

A) the beams from both images are polarized.
B) calcite has different indices of refraction for the two beams.
C) there is interference between the two beams.
D) the calcite has increased the resolving power of your eye.
E) the appearance is due to diffraction.

Question 68

A 60 $\degree$ prism has a refractive index of 1.64 for blue light and 1.61 for red light. Calculate the difference in the angle of incidence for the initial red and blue light ray that is refracted inside the prism and just undergoes total internal reflection at the opposite face of the prism.

A) 4.1 $\degree$
B) 1.5 $\degree$
C) 3.2 $\degree$
D) 2.4 $\degree$
E) 0.4 $\degree$

Question 69

The dependence of the index of refraction on wavelength is called dispersion. A beam of light (in air) containing red and blue light is incident at an angle of 35 $\degree$ 0 on a glass plate that has an index of refraction of 1.64 for blue light and 1.61 for red light. By what percent does the speed of the red light exceed that of the blue light inside the glass, i.e. calculate (v(red)-v(blue) ) * 100 / v(red)?

A) 1.1%
B) 1.8%
C) 0.53%
D) The speed is the same for both colors.
E) 0.019%

Question 70

The dependence of the index of refraction on wavelength is called dispersion. A beam of light (in air) containing red and blue light is incident at an angle of 35 $\degree$ on a glass plate that has an index of refraction of 1.64 for blue light and 1.61 for red light. Calculate the angle between the red and blue light inside the glass.

A) 1.3 $\degree$
B) 0.40 $\degree$
C) 0.56 $\degree$
D) 0.74 $\degree$
E) 0.13 $\degree$

Question 71

Plane-polarized light cannot be produced by

A) dispersion
B) dichroism
C) reflection
D) scattering
E) refraction

Question 72

Light is an electromagnetic wave. When visible light is plane polarized,

A) the electric-field vector is parallel to the magnetic-field vector.
B) the electric-field vector is parallel to the direction of propagation.
C) the electric-field vector is in a fixed direction perpendicular to the direction of propagation, but the magnetic-field vector may be in any direction.
D) the electric-field vector is in a fixed direction perpendicular to the direction of propagation, and the magnetic-field vector is perpendicular to the electric-field vector.
E) None of these is correct.

Question 73

Two polarizers have their transmission axes at an angle $\theta$ . Unpolarized light of intensity I is incident on the first polarizer. What is the intensity of the light transmitted by the second polarizer?

A) I cos² $\theta$
B) 0.5I cos² $\theta$
C) 0.25I cos² $\theta$
D) I cos $\theta$
E) 0.25I cos $\theta$

Question 74

A 60 $\degree$ prism has a refractive index of 1.64 for blue light and 1.61 for red light. Calculate the difference in the angle of emergence from the opposite face of the prism for a beam of red and a beam of blue light that are both incident at an angle of 60^o.

A) 0.4 $\degree$
B) 0.0 $\degree$
C) 1.3 $\degree$
D) 3.9 $\degree$
E) 2.7 $\degree$

Question 75

The index of refraction of a sample of glass cannot be determined by measuring the

A) Brewster's angle.
B) critical angle.
C) angle of minimum deviation.
D) ratio of true to apparent depth.
E) angle of dispersion between red and violet light.

Question 76

The fact that light can be polarized shows that it must be

A) a wave motion.
B) a transverse wave.
C) a longitudinal wave.
D) transmitted by waves of very short length.
E) monochromatic.

Question 77

The index of refraction of water is approximately 1.33. The angle of incidence for maximum polarization by reflection from water is approximately

A) 57º
B) 53º
C) 45º
D) 37º
E) 33º

Question 78

Light known to be polarized in the horizontal direction is incident on a polarizing sheet. It is observed that only 15 percent of the intensity of the incident light is transmitted through the sheet. What angle does the transmission axis of the sheet make with the horizontal?

A) 8.6º
B) 21º
C) 23º
D) 67º
E) 81º

Question 79

When taking a picture of a highly reflecting surface, it is desirable to use a polarizer in front of the camera to cut down on the "glare". Suppose you are taking a picture of a lake where the water is very still. The polarizing axis of the polarizer should ideally be oriented

A) horizontally.
B) vertically.
C) at 30 $\degree$ .
D) at 45 $\degree$ .
E) in any direction.

Question 80

The index of refraction of plate glass is 1.50. The polarizing angle for light incident from air is

A) 8.6º
B) 33.7º
C) 56.3º
D) 81.5º
E) 90º