Electromagnetic Waves Chapter 33 Test Bank Answers Halliday

aChapter: Chapter 33

Learning Objectives

LO 33.1.0 Solve problems related to electromagnetic waves.

LO 33.1.1 In the electromagnetic spectrum, identify the relative wavelengths (longer or shorter) of AM radio, FM radio, television, infrared light, visible light, ultraviolet light, x rays, and gamma rays.

LO 33.1.2 Describe the transmission of an electromagnetic wave by an LC oscillator and an antenna.

LO 33.1.3 For a transmitter with an LC oscillator, apply the relationships between the oscillator’s inductance L, capacitance C, and angular frequency ω, and the emitted wave’s frequency f and wavelength λ.

LO 33.1.4 Identify the speed of an electromagnetic wave in vacuum (and approximately in air).

LO 33.1.5 Identify that electromagnetic waves do not require a medium and can travel through vacuum.

LO 33.1.6 Apply the relationship between the speed of an electromagnetic wave, the straight-line distance traveled by the wave, and the time required for the travel.

LO 33.1.7 Apply the relationships between an electromagnetic wave’s frequency f, wavelength λ, period T, angular frequency ω, and speed c.

LO 33.1.8 Identify that an electromagnetic wave consists of an electric component and a magnetic component that are (a) perpendicular to the direction of travel, (b) perpendicular to each other, and (c) sinusoidal waves with the same frequency and phase.

LO 33.1.9 Apply the sinusoidal equations for the electric and magnetic components of an EM wave, written as functions of position and time.

LO 33.1.10 Apply the relationship between the speed of light c, the permittivity constant ε₀, and the permeability constant μ₀.

LO 33.1.11 For any instant and position, apply the relationship between the electric field magnitude E, the magnetic field magnitude B, and the speed of light c.

LO 33.1.12 Describe the derivation of the relationship between the speed of light c and the ratio of the electric field amplitude E to the magnetic field amplitude B.

LO 33.2.0 Solve problems related to energy transport and the Poynting vector.

LO 33.2.1 Identify that an electromagnetic wave transports energy.

LO 33.2.2 For a target, identify that an EM wave’s rate of energy transport per unit area is given by the Poynting vector , which is related to the cross product of the electric field and magnetic field .

LO 33.2.3 Determine the direction of travel (and thus energy transport) of an electromagnetic wave by applying the cross product for the corresponding Poynting vector .

LO 33.2.4 Calculate the instantaneous rate S of energy flow of an EM wave in terms of the instantaneous electric field magnitude E.

LO 33.2.5 For the electric field component of an electromagnetic wave, relate the rms value E_rms to the amplitude E_m.

LO 33.2.6 Identify an EM wave’s intensity I in terms of energy transport.

LO 33.2.7 Apply the relationships between an EM wave’s intensity I and the electric field’s rms value E_rms and amplitude E_m.

LO 33.2.8 Apply the relationship between average power P_avg, energy transfer ΔE, and the time Δt taken by that transfer, and apply the relationship between the instantaneous power P and the rate of energy of energy transfer dE/dt.

LO 33.2.9 Identify an isotropic point source of light.

LO 33.2.10 For an isotropic point source of light, apply the relationship between the emission power P, the distance r to a point of measurement, and the intensity I at that point.

LO 33.2.11 In terms of energy conservation, explain why the intensity from an isotropic point source of light decreases as 1/r².

LO 33.3.0 Solve problems related to radiation pressure.

LO 33.3.1 Distinguish between force and pressure.

LO 33.3.2 Identify that an electromagnetic wave transports momentum and can exert a force and a pressure on a target.

LO 33.3.3 For a uniform electromagnetic beam that is perpendicular to a target area, apply the relationships between that area, the wave’s intensity, and the force on the target, for both total absorption and total backward reflection.

LO 33.3.4 For a uniform electromagnetic beam that is perpendicular to a target area, apply the relationships between the wave’s intensity and the pressure on the target, for both total absorption and total backward reflection.

LO 33.4.0 Solve problems related to polarization.

LO 33.4.1 Distinguish between polarized light and unpolarized light.

LO 33.4.2 For a light beam headed toward you, sketch representations of polarized light and unpolarized light.

LO 33.4.3 When a beam is sent into a polarizing sheet, explain the function of the sheet in terms of its polarizing direction (or axis) and the electric field component that is absorbed and the component that is transmitted.

LO 33.4.4 For light that emerges from a polarizing sheet, identify its polarization relative to the sheet’s polarizing direction.

LO 33.4.5 For a light beam incident perpendicularly on a polarizing sheet, apply the one-half rule and the cosine-squared rule, distinguishing their uses.

LO 33.4.6 Distinguish between a polarizer and an analyzer.

LO 33.4.7 Explain what is meant if two sheets are crossed.

LO 33.4.8 When a beam is sent into a system of polarizing sheets, work through the sheets one by one, finding the transmitted intensity and polarization.

LO 33.5.0 Solve problems related to reflection and refraction.

LO 33.5.1 With a sketch, show the reflection of a light ray from an interface and identify the incident ray, the reflected ray, the normal, the angle of incidence, and the angle of reflection.

LO 33.5.2 For a reflection, relate the angle of incidence and the angle of reflection.

LO 33.5.3 With a sketch, show the refraction of a light ray at an interface and identify the incident ray, the refracted ray, the normal on each side of the interface, the angle of incidence, and the angle of refraction.

LO 33.5.4 For refraction of light, apply Snell’s law to relate the index of refraction and the angle of the ray on one side of the interface to those quantities on the other side.

LO 33.5.5 In the sketch and using a line along the undeflected direction, show the refraction of light from one material into a second material that has a greater index, a smaller index, and the same index, and, for each situation, describe the refraction in terms of the ray being bent toward the normal, away from the normal, or not at all.

LO 33.5.6 Identify that refraction occurs only at an interface and not in the interior of a material.

LO 33.5.7 Identify chromatic dispersion.

LO 33.5.8 For a beam of red and blue light (or other colors) refracting at an interface, identify which color has the greater bending and which has the greater angle of refraction when they enter a material with a lower index than the initial material and a greater index.

LO 33.5.9 Describe how the primary and secondary rainbows are formed and explain why they are circular arcs.

LO 33.6.0 Solve problems related to total internal reflection.

LO 33.6.1 With sketches, explain total internal reflection and include the angle of incidence, the critical angle, and the relative values of the indexes of refraction on the two sides of the interface.

LO 33.6.2 Identify the angle of refraction for incidence at a critical angle.

LO 33.6.3 For a given pair of indexes of refraction, calculate the critical angle.

LO 33.7.0 Solve problems related to polarization by reflection.

LO 33.7.1 With sketches, explain how unpolarized light can be converted to polarized light by reflection from an interface.

LO 33.7.2 Identify Brewster’s angle.

LO 33.7.3 Apply the relationship between Brewster’s angle and the indexes of refraction on the two sides of an interface.

LO 33.7.4 Explain the function of polarizing sunglasses.

Multiple Choice

1. The theoretical upper limit for the frequency of electromagnetic waves is:

A) just slightly greater than that of red light

B) just slightly less than that of blue light

C) the greatest x-ray frequency

D) none of the above (there is no upper limit)

E) none of the above (but there is an upper limit)

Difficulty: E

Section: 33-1

Learning Objective 33.1.0

2. An electromagnetic wave is generated by:

A) any moving charge

B) any accelerating charge

C) only a charge with changing acceleration

D) only a charge moving in a circle

E) only a charge moving in a straight line

Difficulty: E

Section: 33-1

Learning Objective 33.1.0

3. An electromagnetic wave is traveling in the positive x direction with its electric field along the z axis and its magnetic field along the y axis. The fields are related by:

A) E/x = ₀₀B/x

B) E/x = ₀₀B/t

C) B/x = ₀₀E/x

D) B/x = ₀₀E/t

E) B/x = –₀₀E/t

Difficulty: E

Section: 33-1

Learning Objective 33.1.0

4. Select the correct statement:

A) ultraviolet light has a longer wavelength than infrared

B) blue light has a higher frequency than X rays

C) radio waves have a higher frequency than gamma rays

D) gamma rays have a higher frequency than infrared waves

E) electrons are a type of electromagnetic wave

Difficulty: E

Section: 33-1

Learning Objective 33.1.1

5. Consider radio waves (r), visible light (v), infrared (i), X rays (x), and ultraviolet (u). In order of increasing frequency, they are:

A) r, v, i, x, u

B) r, i, v, u, x

C) i, r, v, u, x

D) x, u, v, i, r

E) r, i, v, x, u

Difficulty: E

Section: 33-1

Learning Objective 33.1.1

6. The order of increasing wavelength for blue (b), green (g), red (r), and yellow (y) light is:

A) r, y, g, b

B) r, g, y, b

C) g, y, b, r

D) b, g, y, r

E) b, y, g, r

Difficulty: E

Section: 33-1

Learning Objective 33.1.1

7. Of the following human eyes are most sensitive to:

A) red light

B) violet light

C) blue light

D) green light

E) none of these (they are equally sensitive to all colors)

Difficulty: E

Section: 33-1

Learning Objective 33.1.1

8. Radio waves differ from visible light waves in that radio waves:

A) travel slower

B) have a higher frequency

C) travel faster

D) have a lower frequency

E) require a material medium

Difficulty: E

Section: 33-1

Learning Objective 33.1.1

9. A transmitter consists of an LC circuit with an inductance of 15 µH and a capacitance of 23 pF. What is the wavelength of the electromagnetic waves it emits?

A) 29 mm

B) 65 mm

C) 5.6 m

D) 35 m

E) 220 m

Difficulty: M

Section: 33-1

Learning Objective 33.1.3

10. Which of the following is NOT true for electromagnetic waves?

A) they consist of changing electric and magnetic fields

B) they travel at different speeds in vacuum, depending on their frequency

C) they transport energy

D) they transport momentum

E) they can be reflected

Difficulty: E

Section: 33-1

Learning Objective 33.1.4

11. Maxwell's equations predict that the speed of light in free space is:

A) an increasing function of frequency

B) a decreasing function of frequency

C) independent of frequency

D) a function of the distance from the source

E) a function of the size of the source

Difficulty: E

Section: 33-1

Learning Objective 33.1.4

12. The speed of light in vacuum is about:

A) 1100 ft/s

B) 93  10⁶ mi/s

C) 6  10²³ m/s

D) 3  10¹⁰ cm/s

E) 186,000 mph

Difficulty: E

Section: 33-1

Learning Objective 33.1.4

13. Which of the following types of electromagnetic radiation travels at the greatest speed in vacuum?

A) Radio waves

B) Visible light

C) X rays

D) Gamma rays

E) All of these travel at the same speed

Difficulty: E

Section: 33-1

Learning Objective 33.1.4

14. The sun is about 1.5  10¹¹ m away. The time for light to travel this distance is about:

A) 4.5  10¹⁹ s

B) 8 s

C) 8 min

D) 8 hr

E) 8 yr

Difficulty: E

Section: 33-1

Learning Objective 33.1.6

15. The time for a radar signal to travel to the Moon and back, a one-way distance of about 3.8  10⁸ m, is:

A) 1.3 s

B) 2.5 s

C) 8 s

D) 8 min

E) 1  10⁶ s

Difficulty: E

Section: 33-1

Learning Objective 33.1.6

16. Visible light has a frequency of about:

A) 5  10¹⁸ Hz

B) 5  10¹⁶ Hz

C) 5  10¹⁴ Hz

D) 5  10¹² Hz

E) 5  10¹⁰ Hz

Difficulty: E

Section: 33-1

Learning Objective 33.1.7

17. Radio waves of wavelength 3 cm have a frequency of:

A) 1 MHz

B) 9 MHz

C) 100 MHz

D) 900 MHz

E) 10,000 MHz

Difficulty: E

Section: 33-1

Learning Objective 33.1.7

18. Radio waves of wavelength 300 m have a frequency of:

A) 10^–6 kHz

B) 108 kHz

C) 500 kHz

D) 1 MHz

E) 9 MHz

Difficulty: E

Section: 33-1

Learning Objective 33.1.7

19. If the electric field in a plane electromagnetic wave is given by E_msin[(3  10⁶ m^–1 x) – t], the value of is:

A) 0.01 rad/s

B) 10 rad/s

C) 100 rad/s

D) 9  10¹⁴ rad/s

E) 9  10¹⁶ rad/s

Difficulty: E

Section: 33-1

Learning Objective 33.1.7

20. The electric field for a plane electromagnetic wave traveling in the +y direction is shown. Consider a point where is in the +z direction. The field is:

A) in the +x direction and in phase with the field

B) in the –x direction and in phase with the field

C) in the +x direction and 1/4 wave out of phase with the field

D) in the +z direction and in phase with the field

E) in the +z direction and 1/4 wave out of phase with the field

Difficulty: E

Section: 33-1

Learning Objective 33.1.8

21. The product µ₀ε₀ has the same units as:

A) (velocity)²

B) (velocity)^1/2

C) 1/velocity

D) 1/velocity²

E) 1/velocity^1/2

Difficulty: E

Section: 33-1

Learning Objective 33.1.10

22. Maxwell's equations predict that the speed of electromagnetic waves in free space is given by:

A) µ₀ε₀

B) (µ₀ε₀)^1/2

C) 1/ µ₀ε₀

D) 1/(µ₀ε₀)^1/2

E) 1/(µ₀ε₀)²

Difficulty: E

Section: 33-1

Learning Objective 33.1.10

23. In a plane electromagnetic wave in vacuum, the ratio E/B of the amplitudes in SI units of the two fields is:

A) the speed of light

B) an increasing function of frequency

C) a decreasing function of frequency

D)

E) 1/

Difficulty: E

Section: 33-1

Learning Objective 33.1.11

24. If the magnetic field in a plane electromagnetic wave is along the y axis and its magnitude is given by B_m sin (kx – t) in SI units, then the electric field is along the z axis and its magnitude is given by

A) (cB_m) cos (kx – t)

B) –(cB_m) cos (kx – t)

C) (cB_m) sin (kx – t)

D) –(cB_m) sin (kx – t)

E) B_m cos (kx – t)

Difficulty: E

Section: 33-1

Learning Objective 33.1.11

25. If the electric field in a plane electromagnetic wave is along the y axis and its magnitude is given by E_m sin (kx + t) in SI units, then the magnetic field is along the z axis and its magnitude is given by:

A) (E_m/c) cos (kx + t)

B) –(E_m/c) cos (kx + t)

C) (E_m/c) sin (kx + t)

D) –(E_m/c) sin (kx + t)

E) E_m cos (kx + t)

Difficulty: E

Section: 33-1

Learning Objective 33.1.11

26. If the amplitude of the electric field in a plane electromagnetic wave is 100 V/m then the amplitude of the magnetic field is:

A) 3.3  10^–7 T

B) 6.7  10^–7 T

C) 0.27 T

D) 8.0  10⁷ T

E) 3.0  10¹⁰ T

Difficulty: E

Section: 33-1

Learning Objective 33.1.11

27. The dimensions of are:

A) J/m²

B) J/s

C) W/s

D) W/m²

E) J/m³

Difficulty: E

Section: 33-2

Learning Objective 33.2.0

28. The time averaged energy in a sinusoidal electromagnetic wave is:

A) overwhelmingly electrical

B) slightly more electrical than magnetic

C) equally divided between the electric and magnetic fields

D) slightly more magnetic than electrical

E) overwhelmingly magnetic

Difficulty: E

Section: 33-2

Learning Objective 33.2.0

29. The rate of energy transport of an electromagnetic wave per unit area is given by:

A) the vector

B) the Poynting vector

C) the Poynting vector divided by the area

D) the Poynting vector divided by time

E) the Poynting vector multiplied by time

Difficulty: E

Section: 33-2

Learning Objective 33.2.2

30. For an electromagnetic wave the direction of the vector gives:

A) the direction of the electric field

B) the direction of the magnetic field

C) the direction of wave propagation

D) the direction of the electromagnetic force on a proton

E) the direction of the emf induced by the wave

Difficulty: E

Section: 33-2

Learning Objective 33.2.3

31. At a certain point and a certain time the electric field of an electromagnetic wave is in the negative z direction and the magnetic field is in the positive y direction. Which of the following statements is true?

A) Energy is being transported in the positive x direction but half a cycle later, when the electric field is in the opposite direction, it will be transported in the negative x direction.

B) Energy is being transported in the positive x direction and half a cycle later, when the electric field is in the opposite direction, it will still be transported in the positive x direction.

C) Energy is being transported in the negative x direction but half a cycle later, when the electric field is in the opposite direction, it will be transported in the positive x direction.

D) Energy is being transported in the negative x direction and half a cycle later, when the electric field is in the opposite direction, it will still be transported in the negative x direction.

E) None of the above is true.

Difficulty: E

Section: 33-2

Learning Objective 33.2.3

32. An electromagnetic wave is transporting energy in the negative y direction. At one point and one instant the magnetic field is in the positive x direction. The electric field at that point and instant is:

A) positive y direction

B) negative y direction

C) positive z direction

D) negative z direction

E) negative x direction

Difficulty: E

Section: 33-2

Learning Objective 33.2.3

33. A sinusoidal electromagnetic wave has an electric field whose rms value is 100 V/m. What is the instantaneous rate S of energy flow for this wave?

A) 1.7  10^–4 W/m²

B) 13 W/m²

C) 27 W/m²

D) 1.0  10⁵ W/m²

E) 4.0  10¹⁰ W/m²

Difficulty: M

Section: 33-2

Learning Objective 33.2.4

34. The magnetic field in a sinusoidal light wave has an amplitude of 3.3  10^–7 T. The intensity of the wave is:

A) 1.7  10^–4 W/m²

B) 13 W/m²

C) 27 W/m²

D) 1.0  10⁵ W/m²

E) 4.0  10¹⁰ W/m²

Difficulty: M

Section: 33-2

Learning Objective 33.2.7

35. A sinusoidal electromagnetic wave with an electric field amplitude of 100 V/m is incident normally on a surface with an area of 1 cm² and is completely absorbed. The energy absorbed in 10 s is:

A) 1.3 mJ

B) 13 mJ

C) 27 mJ

D) 130 mJ

E) 270 mJ

Difficulty: M

Section: 33-2

Learning Objective 33.2.8

36. A point source emits electromagnetic energy at a rate of 100 W. The intensity 10 m from the source is:

A) 10 W/m²

B) 1.6 W/m²

C) 1.0 W/m²

D) 0.080 W/m²

E) 0.024W/m²

Difficulty: M

Section: 33-2

Learning Objective 33.2.10

37. The light intensity 10 m from a point source is 1000 W/m². The intensity 100 m from the same source is:

A) 1000 W/m²

B) 100 W/m²

C) 10 W/m²

D) 1 W/m²

E) 0.1 W/m²

Difficulty: M

Section: 33-2

Learning Objective 33.2.10

38. When the distance between a point source of light and a light meter is reduced from 6.0 m to 2.0 m, the intensity of illumination at the meter will be the original value multiplied by:

A) 3

B) 9

C) 1/3

D) 1/9

E) 1

Difficulty: M

Section: 33-2

Learning Objective 33.2.10

39. Evidence that electromagnetic waves carry momentum is:

A) the tail of a comet points away from the sun

B) electron flow through a wire generates heat

C) a charged particle in a magnetic field moves in a circular orbit

D) heat can be generated by rubbing two sticks together

E) the Doppler effect

Difficulty: E

Section: 33-3

Learning Objective 33.3.2

40. A company claims to have developed material that absorbs light energy without a transfer of momentum. Such material is:

A) impossible

B) possible, but very expensive

C) inexpensive and already in common use

D) in use by NASA but is not commercially available

E) a breakthrough in high technology

Difficulty: M

Section: 33-3

Learning Objective 33.3.2

41. Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is decreased:

A) the radiation pressure increases and the radiation force increases

B) the radiation pressure increases and the radiation force decreases

C) the radiation pressure stays the same and the radiation force increases

D) the radiation pressure stays the same and the radiation force decreases

E) the radiation pressure decreases and the radiation force decreases

Difficulty: E

Section: 33-3

Learning Objective 33.3.3

42. Light with an intensity of 1 kW/m² falls normally on a surface with an area of 1 cm² and is completely absorbed. The force of the radiation on the surface is:

A) 3.3  10^–11 N

B) 1.7  10^–10 N

C) 3.3  10^–10 N

D) 6.7  10^–10 N

E) 1.0  10^–4 N

Difficulty: M

Section: 33-3

Learning Objective 33.3.3

43. Light with an intensity of 1 kW/m² falls normally on a surface with an area of 1 cm² and is completely reflected. The force of the radiation on the surface is:

A) 3.3  10^–11 N

B) 1.7  10^–10 N

C) 3.3  10^–10 N

D) 6.7  10^–10 N

E) 1.0  10^–4 N

Difficulty: M

Section: 33-3

Learning Objective 33.3.3

44. Light with an intensity of 1 kW/m² falls normally on a surface and is completely absorbed. The radiation pressure is:

A) 1 kPa

B) 3  10¹¹ Pa

C) 1.7  10^–6 Pa

D) 3.3  10^–6 Pa

E) 6.7  10^–6 Pa

Difficulty: M

Section: 33-3

Learning Objective 33.3.4

45. Light with an intensity of 1 kW/m² falls normally on a surface and is completely reflected. The radiation pressure is:

A) 1 kPa

B) 3  10¹¹ Pa

C) 1.7  10^–6 Pa

D) 3.3  10^–6 Pa

E) 6.7  10^–6 Pa

Difficulty: M

Section: 33-3

Learning Objective 33.3.4

46. Polarization experiments provide evidence that light is:

A) a longitudinal wave

B) a stream of particles

C) a transverse wave

D) some type of wave

E) nearly monochromatic

Difficulty: E

Section: 33-4

Learning Objective 33.4.0

47. A vertical automobile radio antenna is sensitive to electric fields that are polarized:

A) horizontally

B) in circles around the antenna

C) vertically

D) normal to the antenna in the forward direction

E) none of the above

Difficulty: E

Section: 33-4

Learning Objective 33.4.0

48. For linearly polarized light the plane of polarization is:

A) perpendicular to both the direction of polarization and the direction of propagation

B) perpendicular to the direction of polarization and parallel to the direction of propagation

C) parallel to the direction of polarization and perpendicular to the direction of propagation

D) parallel to both the direction of polarization and the direction of propagation

E) none of the above

Difficulty: E

Section: 33-4

Learning Objective 33.4.0

49. Light from any ordinary source (such as a flame) is usually:

A) unpolarized

B) plane polarized

C) circularly polarized

D) elliptically polarized

E) monochromatic

Difficulty: E

Section: 33-4

Learning Objective 33.4.0

50. The electric field in unpolarized light:

A) has no direction at any time

B) rotates rapidly

C) is always parallel to the direction of propagation

D) can be in any direction perpendicular to the direction of propagation

E) remains along the same line but reverses direction randomly and often

Difficulty: E

Section: 33-4

Learning Objective 33.4.0

51. A clear sheet of polarizing material is placed on top of a second, similar sheet so that their polarizing axes make an angle of 30 with each other. The ratio of the intensity of emerging light to incident unpolarized light is:

A) 1:4

B) 1:3

C) 1:2

D) 3:4

E) 3:8

Difficulty: M

Section: 33-4

Learning Objective 33.4.5

52. An unpolarized beam of light has intensity I₀. It is incident on two ideal polarizing sheets. The angle between the axes of polarization of these sheets is . Find if the emerging light has intensity I₀/4:

A) sin^–1(1/2)

B) sin^-1(1/)

C) cos^–1(1/2)

D) cos^–1(1/)

E) tan^–1(1/4)

Difficulty: M

Section: 33-4

Learning Objective 33.4.5

53. The diagrams show four pairs of polarizing sheets, with the polarizing directions indicated by dashed lines. The two sheets of each pair are placed one behind the other and the front sheet is illuminated by unpolarized light. The incident intensity is the same for all pairs of sheets. Rank the pairs according to the intensity of transmitted light, least to greatest.

A) 1, 2, 3, 4

B) 4, 2, 1, 3

C) 2, 4, 3, 1

D) 2, 4, 1, 3

E) 3, 1, 4, 2

Difficulty: M

Section: 33-4

Learning Objective 33.4.8

54. In a stack of three polarizing sheets the first and third are crossed while the middle one has its axis at 45 to the axes of the other two. The fraction of the intensity of an incident unpolarized beam of light that is transmitted by the stack is:

A) 1/2

B) 1/3

C) 1/4

D) 1/8

E) 0

Difficulty: M

Section: 33-4

Learning Objective 33.4.8

55. Three polarizing sheets are placed in a stack with the polarizing directions of the first and third perpendicular to each other. What angle should the polarizing direction of the middle sheet make with the polarizing direction of the first sheet to obtain maximum transmitted intensity when unpolarized light is incident on the stack?

A) 0°

B) 30

C) 45

D) 60

E) 90

Difficulty: M

Section: 33-4

Learning Objective 33.4.8

56. Three polarizing sheets are placed in a stack with the polarizing directions of the first and third perpendicular to each other. Which of the following angles should the polarizing direction of the middle sheet make with the polarizing direction of the first sheet to obtain zero transmitted intensity when unpolarized light is incident on the stack?

A) 0°

B) 30

C) 45

D) 60

E) all angles allow light to pass through

Difficulty: M

Section: 33-4

Learning Objective 33.4.8

57. The relation _incident = _reflected, which applies as a ray of light strikes an interface between two media, is known as:

A) Faraday's law

B) Snell's law

C) Ampere's law

D) Cole's law

E) none of these

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

58. The relation n₁sin ₁ = n₂ sin ₂ which applies as a ray of light strikes an interface between two media, is known as:

A) Gauss' law

B) Snell's law

C) Faraday's law

D) Cole's law

E) law of sines

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

59. The index of refraction of a substance is:

A) the speed of light in the substance

B) the angle of refraction

C) the angle of incidence

D) the speed of light in vacuum divided by the speed of light in the substance

E) measured in radians

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

60. The units of index of refraction are:

A) m/s

B) s/m

C) radian

D) m/s²

E) none of these

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

61. When light travels from medium X to medium Y as shown:

A) both the speed and the frequency decrease

B) both the speed and the frequency increase

C) both the speed and the wavelength decrease

D) both the speed and the wavelength increase

E) both the wavelength and the frequency are unchanged

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

62. As light goes from one medium to another, it is bent away from the normal. Then:

A) the speed of the light has increased

B) dispersion must occur

C) the second medium has a higher index of refraction

D) no change in speed has occurred

E) refraction has not occurred because refraction means a bending toward the normal

Difficulty: E

Section: 33-5

Learning Objective 3.5.0

63. A pole stands in a river, half in and half out of the water. Another pole of the same length stands vertically on the shore at a place where the ground is level. The shadow cast by the pole in the river on the river bottom is:

A) slightly longer than the shadow of the pole on land

B) much longer than the shadow of the pole on land

C) shorter than the shadow of the pole on land

D) shorter than the shadow of the pole on land if the sun is high and longer if the sun is low

E) the same length as the shadow of the pole on land

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

64. A ray of light passes obliquely through a plate of glass having parallel faces. The emerging ray:

A) is totally internally reflected

B) is bent more toward the normal than the incident ray

C) is bent further away from the normal than the incident ray

D) is parallel to the incident ray but displaced sideways

E) lies on the same straight line as the incident ray

Difficulty: E

Section: 33-5

Learning Objective 33.5.0

65. As used in the laws of reflection and refraction, the "normal" direction is:

A) any convenient direction

B) tangent to the interface

C) along the incident ray

D) perpendicular to the electric field vector of the light

E) perpendicular to the interface

Difficulty: E

Section: 33-5

Learning Objective 33.5.1

66. When an electromagnetic wave meets a reflecting surface, the direction taken by the reflected wave is determined by:

A) the material of the reflecting surface

B) the angle of incidence

C) the index of the medium

D) the intensity of the wave

E) the wavelength

Difficulty: E

Section: 33-5

Learning Objective 33.5.2

67. The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is:

A) 0.53

B) 0.82

C) 1.2

D) 1.9

E) 3.0

Difficulty: M

Section: 33-5

Learning Objective 33.5.4

68. If n_water = 1.33, what is the angle of refraction for the ray shown?

A) 19

B) 22

C) 40

D) 42

E) 48

Difficulty: M

Section: 33-5

Learning Objective 33.5.4

69. The index of refraction for diamond is 2.5. Which of the following is correct for the situation shown?

A) (sin a)/(sin b) = 2.5

B) (sin b)/(sin d) = 2.5

C) (cos a)/(cos c) = 2.5

D) (sin a)/(sin c) = 1/(2.5)

E) a/c = 2.5

Difficulty: E

Section: 33-5

Learning Objective 33.5.4

70. When light passes from air to glass, it bends:

A) toward the normal without changing speed

B) toward the normal and slows down

C) toward the normal and speeds up

D) away from the normal and slows down

E) away from the normal and speeds up

Difficulty: E

Section: 33-5

Learning Objective 33.5.4

71. Which diagram below illustrates the path of a light ray as it travels from a given point X in air to another given point Y in glass?

A) I

B) II

C) III

D) IV

E) V

Difficulty: E

Section: 33-5

Learning Objective 33.5.5

72. A ray of light passes through three media as shown. The speeds of light in these media obey:

A) v₁ > v₂ > v₃

B) v₃ > v₂ > v₁

C) v₃ > v₁ > v₂

D) v₂ > v₁ > v₃

E) v₁ > v₃ > v₂

Difficulty: E

Section: 33-5

Learning Objective 33.5.5

73. The separation of white light into colors by a prism is associated with:

A) total internal reflection

B) partial reflection from each surface

C) variation of index of refraction with wavelength

D) a decrease in the speed of light in the glass

E) selective absorption of various colors

Difficulty: E

Section: 33-5

Learning Objective 33.5.7

74. The rectangular metal tank shown is filled with an unknown liquid. The observer, whose eye is level with the top of the tank, can just see corner E. The index of refraction of this liquid is:

A) 1.75

B) 1.67

C) 1.50

D) 1.33

E) 1.25

Difficulty: M

Section: 33-6

Learning Objective 33.6.1

75. The critical angle for total internal reflection at a diamond-air interface is 25. Suppose light is incident at an angle of with the normal. Total internal reflection will occur if the incident medium is:

A) air and = 25

B) air and > 25

C) air and < 25

D) diamond and < 25

E) diamond and > 25

Difficulty: M

Section: 33-6

Learning Objective 33.6.2

76. The diagram shows total internal reflection. Which of the following statements is NOT true?

A) angle AON is the angle of incidence

B) angle AON = angle BON

C) angle AON must be the critical angle

D) the speed of light in medium II is greater than that in medium I

E) if angle AON were increased, there would still be total internal reflection

Difficulty: E

Section: 33-6

Learning Objective 33.6.2

77. The index of refraction of benzene is 1.80. The critical angle for total internal reflection, at a benzene-air interface, is about:

A) 56

B) 47

C) 34

D) 22

E) 18

Difficulty: M

Section: 33-6

Learning Objective 33.6.3

78. The index of refraction of a certain glass is 1.50. The sine of the critical angle for total internal reflection at a glass-air interface is:

A) 0.50

B) 0.67

C) 0.75

D) 1.00

E) 1.50

Difficulty: M

Section: 33-6

Learning Objective 33.6.3

79. The illustration shows total internal reflection taking place in a piece of glass. The index of refraction of this glass:

A) is at least 2.0

B) is at most 2.0

C) is at least 1.15

D) is at most 1.15

E) cannot be calculated from the given data

Difficulty: M

Section: 33-6

Learning Objective 33.6.3

80. If n_water = 1.33 and n_glass = 1.50, then total internal reflection at an interface between this glass and water:

A) occurs whenever the light goes from glass to water

B) occurs whenever the light goes from water to glass

C) may occur when the light goes from glass to water

D) may occur when the light goes from water to glass

E) can never occur at this interface

Difficulty: E

Section: 33-6

Learning Objective 33.6.3

81. A ray of light in water (index n₁) is incident on its surface (with air) at the critical angle. Some oil (index n₂) is now floated on the water. The angle between the ray in the oil and the normal is:

A) sin^–1(1.00)

B) sin^–1(1/n₁)

C) sin^–1(1/n₂)

D) sin^–1(n₁/n₂)

E) sin^–1(n₂/n₁)

Difficulty: M

Section: 33-6

Learning Objective 33.6.3

82. For a beam of light in air (n = 1) reflecting off glass (n = 1.5), what is Brewster’s angle?

A) 34°

B) 42°

C) 45°

D) 48°

E) 56°

Difficulty: E

Section: 33-7

Learning Objective 33.7.3

83. Why do polarizing sunglasses work to reduce glare?

A) They don’t; this is just a marketing ploy

B) They reduce the amount of light entering your eyes

C) Light reflected from horizontal surfaces tends to be horizontally polarized, so the sunglasses’ vertical polarization cuts the glare

D) Light reflected from horizontal surfaces tends to be vertically polarized, so the sunglasses’ horizontal polarization cuts the glare

E) Light reflected from horizontal surfaces tends to be horizontally polarized, so the sunglasses’ horizontal polarization cuts the glare

Difficulty: E

Section: 33-7

Learning Objective 33.7.4