Deck 32: The Nature and Propagation of Light

Question 1

Unpolarized light is incident upon two polarization filters that do not have their transmission axes aligned. If 18% of the light passes through this combination of filters, what is the angle between the transmission axes of the filters?

A) 53°
B) 73°
C) 85°
D) 80°

Answer 1

53°

Question 2

Light strikes a 5.0-cm thick sheet of glass at an angle of incidence in air of 50°. The sheet has parallel faces and the glass has an index of refraction 1.50.
(a) What is the angle of refraction in the glass?
(b) After traveling through the glass the light re-emerges into the air. What is the final angle of refraction in air?
(c) As it leaves the glass, by what distance is the path of the ray is displaced from what it was before entering the glass?

Answer 2

(a) 31°
(b) 50°
(c) 1.9 cm

Question 3

Light of intensity I₀ and polarized horizontally passes through three polarizes. The first and third polarizing axes are horizontal, but the second one is oriented 20.0° to the horizontal. In terms of I₀, what is the intensity of the light that passes through the set of polarizers?

A) 0.780I₀
B) 0.180I₀
C) 0.442I₀
D) 0.883I₀

Answer 3

0.780I₀

Question 4

The critical angle in air for a particular type of glass is 39.0°. What is the speed of light in this class glass? (c = 3.00 × 10⁸ m/s)

A) 1.97 × 10⁸ m/s
B) 1.94 × 10⁸ m/s
C) 1.91 × 10⁸ m/s
D) 1.89 × 10⁸ m/s
E) 2.00 × 10⁸ m/s

Question 5

Unpolarized light passes through three polarizing filters. The first one is oriented with a horizontal transmission axis, the second filter has its transmission axis 25.7° from the horizontal, and the third one has a vertical transmission axis. What percent of the light gets through this combination of filters?

A) 7.6%
B) 92.4%
C) 50.0%
D) 0.00%

Question 6

A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 10⁸ m/s)

Question 7

Light in air is initially traveling parallel to the face AC of an equilateral triangular prism, as shown in the figure. The prism is made of glass with an index of refraction of 1.52. If the light does not strike the face AC, what is the angle between the ray as it leaves the prism at face BC and the normal in air at that face?

A) 83°
B) 19°
C) 59°
D) 27°
E) 55°

Question 8

A glass plate whose index of refraction is 1.56 is immersed in a liquid. The surface of the glass is inclined at an angle of 42.0° with the vertical. A horizontal ray in the glass is incident on the interface. When the liquid is a certain alcohol, the incident ray arrives at the interface at the critical angle. What is the index of refraction of the alcohol?

A) 1.04
B) 1.02
C) 1.00
D) 0.984
E) 1.06

Question 9

Polarized light passes through a polarizer. If the electric vector of the polarized light is horizontal what, in terms of the initial intensity I₀, is the intensity of the light that passes through a polarizer if the polarizer is tilted 22.5° from the horizontal?

A) 0.854I₀
B) 0.147I₀
C) 0.191I₀
D) 0.011I₀

Question 10

An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for the oil is 1.15, and for water it is 1.33.)

A) 27°
B) 32°
C) 36°
D) 39°
E) 52°

Question 11

What is the critical angle for light traveling from crown glass (n = 1.52) into water (n = 1.33)?

A) 42°
B) 48°
C) 53°
D) 57°
E) 61°

Question 12

When light goes from one material into another material having a HIGHER index of refraction

A) its speed, wavelength, and frequency all decrease.
B) its speed and wavelength decrease, but its frequency stays the same.
C) its speed decreases but its wavelength and frequency both increase.
D) its speed decreases but its frequency and wavelength stay the same.
E) its speed increases, its wavelength decreases, and its frequency stays the same.

Question 13

The speed of light in a material is 0.50c. What is the critical angle of a light ray at the interface between the material and a vacuum?

A) 30°
B) 21°
C) 24°
D) 27°

Question 14

In the figure, a laser positioned on a ship is used to communicate with a small two-man research submarine resting on the bottom of a lake. The laser is positioned 12 m above the surface of the water, and it strikes the water 20 m from the side of the ship. The water is 76 m deep and has an index of refraction of 1.33. How far horizontally is the submarine from the side of the ship?

A) 84.1 m
B) 64.1 m
C) 104 m
D) 74.1 m
E) 94.1 m

Question 15

A tank holds a 1.44-m thick layer of oil that floats on a 0.96-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.40 and 1.52, respectively. A ray originating at O crosses the brine-oil interface at a point 0.60 m from the axis. The ray continues and emerges into the air above the oil. What is the angle that the ray in the air makes with the vertical?

A) 48°
B) 51°
C) 54°
D) 57°
E) 60°

Question 16

Which one of the following is an accurate statement about light?

A) When light strikes a surface at Brewster's angle, the reflected and transmitted light are both 100% polarized.
B) When light strikes a surface at Brewster's angle, it is completely reflected at the surface.
C) When light strikes a surface at Brewster's angle, only the reflected light is 100% polarized.
D) When light strikes a surface at the critical angle, only the reflected light is 100% polarized.
E) When light strikes a surface at the critical angle, all the light passes through the surface.

Question 17

An optic fiber is made of clear plastic with index of refraction of 1.50, surrounded by air. For what angles of incidence θ will light remain within the plastic fiber?

A) θ ≥ 21.1°
B) θ < 38.3°
C) θ > 38.3°
D) θ < 41.8°
E) θ > 41.8°

Question 18

A ray of light strikes a boundary between two transparent materials, and there is no transmitted ray, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

A) n₁ ≥ n₂
B) n₁ > n₂
C) n₁ = n₂
D) n₂ ≥ n₁
E) n₂ > n₁

Question 19

A ray of light goes from one transparent material into another, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

A) n₁ ≥ n₂
B) n₁ > n₂
C) n₁ = n₂
D) n₂ ≥ n₁
E) n₂ > n₁

Question 20

An optical fiber made of glass with an index of refraction 1.50 is coated with a plastic with index of refraction 1.30. What is the critical angle of this fiber at the glass-plastic interface?

A) 90.0°
B) 41.8°
C) 60.1°
D) 50.2°
E) 61.1°

Question 21

A ray of light traveling in air strikes the surface of a certain plastic slab at 63.0° with respect to the normal in air. It travels in the plastic slab at a 30.6° angle with respect to the normal. Find the critical angle for the plastic in air.

Question 22

The following are positioned in sequence: A source of a beam of natural light of intensity I₀; three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, from the perspective of the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. Polarizer B is set so that the beam intensity is zero at the observer. Which of the following pairs of angles are possible axis angle settings of polarizer B?

A) 40° and 90°
B) 40° and 130°
C) 40° and 140°
D) 90° and 130°
E) 90° and 140°

Question 23

In the figure, the orientation of the transmission axis for each of three polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarized with an intensity of 1000 W/m². What is the intensity of the beam after it has passed through the three polarizing sheets when θ₁ = 30°, θ₂ = 30° and θ₃ =60°?

A) 141 W/m²
B) 316 W/m²
C) 433 W/m²
D) 563 W/m²
E) 188 W/m²

Question 24

A tank holds a 1.44-m thick layer of oil that floats on a 0.96-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.40 and 1.52, respectively. A ray originating at O reaches the brine-oil interface at the critical angle. What is the distance of this point from the axis?

A) 1.5 m
B) 1.7 m
C) 1.9 m
D) 2.1 m
E) 2.3 m

Question 25

Light consisting of a mixture of red and blue light enters a 40°, 70°, 70° prism along a line parallel to the side opposite the 40° vertex. The index of refraction of the prism material for blue light is 1.530, and for red light it is 1.525. What is the angle between the two emerging beams of light?

A) 0.5°
B) 0.9°
C) 0.1°
D) 0.3°
E) 0.7°

Question 26

The critical angle for an air-glass interface is 29.6°. When a light ray in air is incident on the interface, the reflected ray is 100% polarized. What is the angle of refraction of that ray?

A) 26.3°
B) 25.7°
C) 25.1°
D) 24.5°
E) 23.9°

Question 27

A ray of light consisting of blue light (wavelength 480 nm) and red light (wavelength 670 nm) is incident on a thick piece of glass at 80°. What is the angular separation between the refracted red and refracted blue beams while they are in the glass? (The respective indices of refraction for the blue light and the red light are 1.4636 and 1.4561.)

A) 0.27°
B) 0.33°
C) 0.36°
D) 0.46°
E) 0.54°

Question 28

A beam of light of two different wavelengths enters a pane of glass 3.00 mm thick at an angle of incidence of 56°. The indices of refraction for the two different colors are 1.514 and 1.528. Because of dispersion, the colored beams, although parallel, are separated by a small distance. How far apart are they?

A) 0.057 mm
B) 0.0083 mm
C) 0.025 mm
D) 0.014 mm
E) 0.0062 mm