Deck 23: Wave Properties of Light

Question 1

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 m/s
B) 60.8 m/s
C) 40.6 m/s
D) 32.4 m/s
E) 26.8 m/s

Answer 1

60.8 m/s

Question 2

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

Answer 2

1, 3, and 4 only

Question 3

When a ray of light traveling in air is incident at θ = 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.

Answer 3

is not described by any of these statements.

Question 4

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 5

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 6

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 7

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.

Question 8

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 9

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 10

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 11

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 12

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 13

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 θ in the water is

A) 42º.
B) 36º.
C) 63º.
D) 49º.
E) 27º.

Question 14

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 15

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? θ₁ and θ₂ are the angles of incidence and refraction.)

A) f₁ sin θ₁ = f₂ sin θ₂
B) f₁v₂ = f₂v₁
C) f₁ = f₂
D) f₁v₁ = f₂v₂
E) f₁ sin θ₂ = f₂ sin θ₁

Question 16

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 17

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 18

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

Question 19

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 m/s
B) 70.8 m/s
C) 61.3 m/s
D) 34.3 m/s
E) 27.7 m/s

Question 20

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 21

The index of refraction is related to the prism angle and the angle of minimum deviation by n = sin ½d + f)/sin ½f
The angle of minimum deviation in the figure is angle

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

Question 22

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 φ in the lower slab is approximately

A) 22º.
B) 30º.
C) 37º.
D) 53º.
E) 60º.

Question 23

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 24

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 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

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 27

The principle of superposition states:

A) The effect observed at each point of a wave made up of two or more waves is the sum of the effects that the individual waves would produce at that point.
B) Huygens' wavelets cannot be allowed to extend across regions where the phase velocity of the wave changes abruptly.
C) Sources of radiation whose phase angles are maintained at constant differences are said to be coherent.
D) A characteristic phenomenon of wave propagation is the tendency of a wave to expand around and behind any obstacles it chances to encounter.
E) A good source of waves at a particular frequency is a good detector of waves at the same frequency.

Question 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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) < 1 = < 2 = < 3 = < 4
B) < 1 = < 2; < 3 = < 4; but < 1 ≠ < 3
C) < 1 = < 2 = < 3; but < 4 ≠ < 1
D) < 1 = < 4; but < 2 ≠ < 4
E) < 1 ≠ < 2 ≠ < 3 ≠ < 4

Question 36

Huygens' theory for the construction of wavefronts states that

A) the angle of incidence is always less than the angle of refraction.
B) the time required for light to travel from one point to another is either a maximum or minimum.
C) only parallel light produces interference and diffraction.
D) each point on a wavefront is itself the source of a secondary spherical wave.
E) all wavefronts are spherical.

Question 37

"To find the value of the resultant displacement for overlapping waves at any point at a particular instant, it is only necessary to add the values of the displacements for the individual waves." This is a statement of

A) Huygens' principle.
B) the principle of superposition.
C) Bernoulli's principle.
D) the principle of dispersion.
E) Newton's theory of light.

Question 38

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 39

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 40

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 θ is less than the angle of total internal reflection.

Question 41

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, Ɵ, 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 42

A helium-neon laser emits light of wavelength 632.8 nm and has a power output of 1.5 mW. How many photons are emitted per second by this laser?

A) 1.34 × 10¹⁴
B) 2.56 × 10¹⁵
C) 3.09 × 10¹⁵
D) 4.22 × 10¹⁵
E) 4.78 × 10¹⁵

Question 43

A ray of light traveling in air enters the end of a rectangular block of a material that has an index of refraction n = 1.35. The largest value of the angle θ 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 44

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 45

The wavelength of light that has a photon energy of 4.25 eV is

A) 292 nm.
B) 973 nm.
C) 706 nm.
D) 1559 nm.
E) None of these is correct.

Question 46

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 47

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

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

Question 48

A helium-neon laser emits light of wavelength 632.8 nm and has a power output of 3 mW. How many photons are emitted per second by this laser?

A) 9.55 × 10¹⁴
B) 9.55 × 10¹⁵
C) 8.24 × 10¹⁵
D) 6.53 × 10¹⁵
E) 4.78 × 10¹⁵

Question 49

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 50

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 51

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 52

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 53

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, Ɵ_c, at the core-cladding interface?

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

Question 54

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 55

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 56

A light wave is like a sound wave in that both

A) are longitudinal waves.
B) are means of transmitting energy.
C) are transverse waves.
D) require a material medium for propagation.
E) have the same velocity in air.

Question 57

The energy of an electromagnetic wave that is in the red region of the visible spectrum is approximately

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

Question 58

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°
B) 66.9°
C) 82.8°
D) 42.6°
E) None of these is correct.

Question 59

The photon energy for light of wavelength 500 nm is approximately

A) 1.77 eV.
B) 3.10 eV.
C) 6.20 eV.
D) 2.48 eV.
E) 5.46 eV.

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 or 4.
E) points 1 or 4.

Question 61

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 62

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 63

A 60° 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°
B) 18.9°
C) 29.4°
D) 30.6°
E) 60.6°

Question 64

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.

Question 65

White light is incident on a prism from the left. After it passes through the first prism, a color spectrum of light is observed. The spectrum is then passed through a second prism, which is inverted compared to the first prism. The color light that exits from the second prism

A) is also a color spectrum and more spread out.
B) is also a color spectrum but less spread out.
C) is white in color.
D) has more colors than the first spectrum.
E) has fewer colors than the first spectrum.

Question 66

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 67

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 68

A 60° 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° to the normal.

A) 24.3°
B) 35.8°
C) 45.1°
D) 48.7°
E) 55.3°

Question 69

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 θ_m, where θ_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 70

A 60° 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°
B) 1.5°
C) 3.2°
D) 2.4°
E) 0.4°

Question 71

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

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

Question 72

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 73

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 74

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° 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 vred)-vblue) ) * 100 / vred)?

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

Question 75

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 76

A 60° 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 light and a beam of blue light that are both incident at an angle of 60⁰.

A) 0.4°
B) 0.0°
C) 1.3°
D) 3.9°
E) 2.7°

Question 77

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° 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°
B) 0.40°
C) 0.56°
D) 0.74°
E) 0.13°

Question 78

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 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°.
D) at 45°.
E) in any direction.

Question 80

Two polarizers have their transmission axes at an angle θ. 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 θ
B) 0.5I cos² θ
C) 0.25I cos² θ
D) I cos θ
E) 0.25I cos θ