Deck 17: Wave Optics

Question 1

A double-slit interference experiment is performed in the air. Later, the same apparatus is immersed in benzene (which has an index of refraction of 1.50), and the experiment is repeated. When the apparatus is in benzene, you observe that the interference fringes are

A) more closely spaced than when the apparatus is in air.
B) equally spaced as when the apparatus is in air.
C) more widely spaced than when the apparatus is in air.

Answer 1

A

Question 2

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the slit width is doubled?

A) It will be cut to one-quarter its original size.
B) It will be cut in half.
C) It will double.
D) It will become four times as large.
E) It will become eight times as large.

Answer 2

B

Question 3

Radio waves are diffracted by large objects such as buildings, whereas light is not noticeably diffracted. Why is this?

A) Radio waves are unpolarized, whereas light is normally polarized.
B) The wavelength of light is much smaller than the wavelength of radio waves.
C) The wavelength of light is much greater than the wavelength of radio waves.
D) Radio waves are coherent and light is usually not coherent.
E) Radio waves are polarized, whereas light is usually unpolarized.

Answer 3

B

Question 4

If a sheet containing a single thin slit is heated (without damaging it) and therefore expands, what happens to the width of the central bright diffraction region on a distant screen?

A) It gets narrower.
B) It gets wider.
C) It doesn't change.

Question 5

What principle is responsible for light spreading as it passes through a narrow slit?

A) refraction
B) polarization
C) diffraction
D) dispersion

Question 6

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum constructive interference is to occur at point P, the two beams must travel paths that differ by

A) a whole number of wavelengths.
B) an odd number of half-wavelengths.
C) a whole number of half-wavelengths.

Question 7

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the wavelength of the illuminating light is doubled?

A) It will be cut to one-quarter its original size.
B) It will be cut in half.
C) It will double.
D) It will become four times as large.
E) It will become eight times as large.

Question 8

Two light sources are said to be coherent if they are

A) of the same frequency.
B) of the same frequency, and maintain a constant phase difference.
C) of the same amplitude, and maintain a constant phase difference.
D) of the same frequency and amplitude.

Question 9

If the index of refraction of a material is 2, this means that light travels

A) 2 times as fast in air as it does in vacuum.
B) 2 times as fast in the material as it does in air.
C) 2 times as fast in vacuum as it does in the material.
D) 2 times as fast in the material than it does in vacuum.
E) 1/2 as fast in air as it does in the material.

Question 10

When light travels from air into water,

A) its velocity, wavelength and frequency all change.
B) its velocity changes, but its frequency and wavelength do not change.
C) its frequency changes, but its velocity and wavelength do not change.
D) its velocity and wavelength change, but its frequency does not change.
E) its wavelength changes, but its velocity and frequency do not change.

Question 11

Monochromatic coherent light shines through a pair of slits. If the wavelength of the light is decreased, which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.)

A) The distance between the maxima stays the same.
B) The distance between the maxima decreases.
C) The distance between the minima stays the same.
D) The distance between the minima increases.
E) The distance between the minima decreases.

Question 12

If a sheet containing a single slit is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction minimum?

A) It moves toward the centerline.
B) It moves away from the centerline.
C) It doesn't change.

Question 13

In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with

A) blue light.
B) green light.
C) yellow light.
D) red light.
E) The separation is the same for all wavelengths.

Question 14

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum destructive interference is to occur at point P, the two beams must travel paths that differ by

A) a whole number of wavelengths.
B) an odd number of half-wavelengths.
C) a whole number of half-wavelengths.

Question 15

What do we mean when we say that two light rays striking a screen are in phase with each other?

A) When the electric field due to one is a maximum, the electric field due to the other is also a maximum, and this relation is maintained as time passes.
B) They are traveling at the same speed.
C) They have the same wavelength.
D) They alternately reinforce and cancel each other.

Question 16

If a sheet containing two very thin slits is heated (without damaging it), what happens to the angular location of the first-order interference minimum?

A) It moves toward the centerline.
B) It moves away from the centerline.
C) It doesn't change.

Question 17

In a single-slit diffraction experiment, the width of the slit through which light passes is reduced. What happens to the width of the central bright fringe in the resulting diffraction pattern?

A) It stays the same.
B) It becomes narrower.
C) It becomes wider.

Question 18

In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm. What happens to the distance between adjacent maxima when the slit separation is cut in half?

A) It increases to 2.0 cm.
B) It increases to 4.0 cm.
C) It decreases to 0.50 cm.
D) It decreases to 0.25 cm.
E) None of these choices are correct.

Question 19

A light beam has speed c in vacuum and speed v in a certain plastic. The index of refraction n of this plastic is

A) n = cv.
B) n = (v/c)².
C) n = v/c.
D) n = c/v.
E) n = (c/v)².

Question 20

Monochromatic coherent light shines through a pair of slits. If the distance between these slits is decreased, which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.)

A) The distance between the maxima stays the same.
B) The distance between the maxima decreases.
C) The distance between the minima stays the same.
D) The distance between the minima increases.
E) The distance between the maxima increases.

Question 21

Light reflects off the surface of Lake Superior. What phase shift does it undergo?

A) 0°
B) 90°
C) 180°
D) 270°
E) It does not undergo any phase shift.

Question 22

If a diffraction grating is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order maximum?

A) It moves toward the centerline.
B) It moves away from the centerline.
C) It doesn't change.

Question 23

Light of wavelength 550 nm in air is found to travel at 1.96 × 10⁸ m/s in a certain liquid. What are the frequency and wavelength of the light in this liquid? (c = 3.0 × 10⁸ m/s)

Question 24

When a beam of light that is traveling in air is reflected by a glass surface, there is

A) a 90° phase change in the reflected beam.
B) no phase change in the reflected beam.
C) a 180° phase change in the reflected beam.
D) a 60° phase change in the reflected beam.
E) a 45° phase change in the reflected beam.

Question 25

Red light with a wavelength of 650 nm travels from air into a liquid with an index of 1.33. What are the frequency and wavelength of the light in the liquid? (c = 3.0 × 10⁸ m/s)

Question 26

Light of wavelength 550 nm in air is found to travel at 1.96 × 10⁸ m/s in a certain liquid. (c = 3.0 × 10⁸ m/s)
(a) What is the index of refraction of this liquid?
(b) What is the frequency of the light in air?

Question 27

When a beam of light that is traveling in glass strikes an air boundary at the surface of the glass, there is

A) a 90° phase change in the reflected beam.
B) no phase change in the reflected beam.
C) a 180° phase change in the reflected beam.
D) a 60° phase change in the reflected beam.
E) a 45° phase change in the reflected beam.

Question 28

The colors on an oil slick are caused by reflection and

A) diffraction.
B) interference.
C) refraction.
D) polarization.
E) ionization.

Question 29

Light having a frequency in vacuum of 6.0 × 10¹⁴ Hz enters a liquid of refractive index 2.0. What is the frequency of the light in this liquid? (c = 3.0 × 10⁸ m/s)

A) 12 × 10¹⁴ Hz
B) 6.0 × 10¹⁴ Hz
C) 3.0 × 10¹⁴ Hz
D) 1.5 × 10¹⁴ Hz
E) 2.0 × 10¹⁴ Hz

Question 30

When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of 3/2, its speed

A) increases by a factor of 3/2.
B) is reduced to 2/3 its original value.
C) is unaffected.

Question 31

Light in a frozen block of ice reflects off the ice-air interface at the surface of the block. What phase shift does it undergo?

A) 0°
B) 90°
C) 180°
D) 270°
E) It does not undergo any phase shift.

Question 32

Which of the following changes would increase the separation between the bright fringes in the diffraction pattern formed by a diffraction grating?

A) Increase the wavelength of the light used.
B) Increase the separation between the slits.
C) Immerse the apparatus in water.
D) All of these.
E) None of these.

Question 33

The index of refraction of a certain glass is measured to be 1.5. What is the speed of light in that glass? (c = 3.0 × 10⁸ m/s)

A) 1.0 × 10⁸ m/s
B) 2.0 × 10⁸ m/s
C) 3.0 × 10⁸ m/s
D) 4.0 × 10⁸ m/s
E) 5.0 × 10⁸ m/s

Question 34

If a metal sheet containing a tiny hole is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction maximum?

A) It moves toward the centerline.
B) It moves away from the centerline.
C) It doesn't change.

Question 35

When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of 3/2, its wavelength

A) increases by a factor of 3/2.
B) is reduced to 2/3 its original value.
C) is unaffected.

Question 36

When a light wave enters into a medium of different refractive index,

A) only its speed and frequency change.
B) only its speed and wavelength change.
C) only its frequency and wavelength change.
D) its speed, frequency, and wavelength change.

Question 37

Light having a speed in vacuum of 3.0 × 10⁸ m/s enters a liquid of refractive index 2.0. In this liquid, its speed will be

A) 6.0 × 10⁸ m/s
B) 3.0 × 10⁸ m/s
C) 1.5 × 10⁸ m/s
D) 0.75 × 10⁸ m/s
E) 0.67 × 10⁸ m/s

Question 38

Light of the same wavelength passes through two diffraction gratings. One grating has 4000 lines/cm, and the other one has 6000 lines/cm. Which grating will spread the light through a larger angle in the first-order pattern?

A) the 4000-line grating
B) the 6000-line grating
C) Both gratings spread the light the same.

Question 39

When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of 3/2, its frequency

A) increases by a factor of 3/2.
B) is reduced to 2/3 its original value.
C) is unaffected.

Question 40

The speed of light in a certain material is measured to be 2.2 × 10⁸ m/s. What is the index of refraction of this material? (c = 3.0 × 10⁸ m/s)

A) 1.1
B) 1.2
C) 1.4
D) 1.6
E) 1.8

Question 41

In a double-slit experiment, the slit separation is 1.75 mm, and two coherent wavelengths of light, 425 nm and 510 nm, illuminate the slits. At what angle from the centerline on either side of the central maximum will a bright fringe from one pattern first coincide with a bright fringe from the other pattern?

Question 42

Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0. In this liquid, what is the wavelength of the light? (c = 3.0 × 10⁸ m/s)

A) 1200 nm
B) 600 nm
C) 300 nm
D) 150 nm
E) 200 nm

Question 43

Coherent light of wavelength 519 nm passes through two slits. In the resulting interference pattern on a screen 4.6 m away, adjacent bright fringes are apart. What is the separation of the two slits?

Question 44

In a two-slit experiment, a third-order bright fringe is observed at an angle of 7.10° away from the centerline. If the wavelength of light is 595 nm, how far apart are the two slits?

A) 1.44 × m
B) 1.07 × m
C) 2.12 × m
D) 2.53 × m
E) 3.76 × m

Question 45

A two-slit arrangement with 60.3 μm separation between the slits is illuminated with 537.0-nm wavelength light. If a viewing screen is located 2.14 m from the slits, find the distance on the screen from the first dark fringe on one side of the central maximum to the second dark fringe on the other side.

A) 57.2 mm
B) 38.1 mm
C) 76.3 mm
D) 26.9 mm

Question 46

Coherent light of wavelength 540 nm passes through a pair of thin slits that are 3.4 × m apart. At what angle away from the centerline does the second bright fringe occur?

A) 1.8°
B) 3.7°
C) 4.3°
D) 1.5°
E) 5.0°

Question 47

In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.20 x m. At what angle away from the centerline does the first bright fringe occur?

A) 1.56°
B) 2.22°
C) 3.12°
D) 4.70°
E) 6.24°

Question 48

A two-slit arrangement with 60.3 μm separation between the slits is illuminated with coherent light. If a viewing screen is located 2.14 m from the slits, find the distance from the first dark fringe on one side of the central maximum to the second dark fringe on the other side.

A) 52.3 mm
B) 34.9 mm
C) 69.7 mm
D) 24.6 mm

Question 49

A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 bright fringes/cm on the screen, what is the wavelength of the monochromatic light?

A) 550 nm
B) 600 nm
C) 650 nm
D) 700 nm
E) 750 nm

Question 50

The distance between two slits is 1.50 × m. A beam of coherent light of wavelength 600 nm illuminates these slits, and the distance between the slit and the screen is 2.00 m. What is the distance on the screen between the central bright fringe and the fourth-order bright fringe?

A) 0.132 m
B) 0.201 m
C) 0.324 m
D) 0.528 m
E) 0.688 m

Question 51

In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.20 × 10^-5 m. At what angle away from the centerline does the second dark fringe occur?

A) 4.70°
B) 3.51°
C) 3.94°
D) 1.17°
E) 2.34°

Question 52

In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.100 mm. If the first-order bright fringe is measured to be 3.40 cm from the centerline, what is the wavelength of the light?

A) 354 nm
B) 241 nm
C) 133 nm
D) 3.09 μm
E) 2.11 μm

Question 53

Coherent light of wavelength 575 nm falls on a double-slit and the third-order bright fringe is seen at an angle of 6.5° away from the centerline. How far apart are the double slits?

A) 5.0 μm
B) 10 μm
C) 15 μm
D) 20 μm

Question 54

A double-slit experiment uses coherent light of wavelength 633 nm with a slit separation of 0.100 mm and a screen placed 2.0 m away.
(a) How wide on the screen is the central bright fringe?
(b) What is the distance on the screen between first-order and second-order bright fringes?
(c) What is the angular separation (in radians) between the central maximum and the first-order maximum?

Question 55

A double slit that is illuminated with coherent light of wavelength 644 nm produces a pattern of bright and dark fringes on a screen 6.00 cm from the slits. If the slits are 2783 nm apart, what is the distance on the screen between the 4^th and the 2^nd bright fringes on one side of the central maximum?

A) 23.0 cm
B) 17.6 cm
C) 11.5 cm
D) 3.13 cm
E) 14.7 cm

Question 56

In a two-slit experiment, the slit separation is 3.00 × m. The interference pattern is created on a screen that is 2.00 m away from the slits. If the 7th bright fringe on the screen is 10.0 cm away from the central fringe, what is the wavelength of the light?

A) 100 nm
B) 204 nm
C) 214 nm
D) 224 nm
E) 234 nm

Question 57

Two thin slits are 6.00 μm apart. Monochromatic coherent light falls on these slits, and produces a fifth-order bright interference fringe at an angle of 32.3° away from the centerline. What is the wavelength of the light?

A) 164 nm
B) 416 nm
C) 614 nm
D) 641 nm

Question 58

A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If the wavelength of the monochromatic light is 450 nm, what is the angular separation between adjacent dark fringes on the screen, measured in milliradians?

A) 0.15 mrad
B) 0.20 mrad
C) 0.25 mrad
D) 0.30 mrad
E) 0.36 mrad

Question 59

In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.0400 mm. If the second order bright fringe is measured to be 4.20 cm from the centerline on the screen, what is the wavelength of light?

A) 200 nm
B) 381 nm
C) 401 nm
D) 620 nm
E) 763 nm

Question 60

An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is from the slits. If the slits are illuminated with coherent light of wavelength 633 nm, how far apart should the slits be?

A) 68.5 μm
B) 74.0 μm
C) 79.5 μm
D) 63.0 μm

Question 61

A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide. At what the angle away from the centerline does the first dark fringe occur?

A) 9.35°
B) 11.4°
C) 12.2°
D) 39.9°
E) 18.7°

Question 62

The figure shows the resulting pattern when a single slit is illuminated by monochromatic light. The slit is 0.3 × m wide and is illuminated by light of wavelength 506 nm. A diffraction pattern is seen on a screen 2.8 m from the slit. What is the linear distance on the screen between the first two diffraction minima on either side of the central diffraction maximum?

Question 63

A beam of monochromatic light passes through a slit that is 11.0 μm wide. If the first order dark fringe of the resulting diffraction pattern is at an angle of 4.31° away from the centerline, what is the wavelength of light?

A) 827 nm
B) 301 nm
C) 602 nm
D) 402 nm
E) 201 nm

Question 64

Two radio antennas are 10 km apart on a north-south axis on high mountain tops at the seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of 4.70 MHz. A steamship, 200 km offshore, travels toward the north at 15 km/h and passes east of the antennas. A radio on board the ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a maximum at a given instant. How much later until the next occurrence of maximum reception? (c = 3.00 × 10⁸ m/s)

A) 5.1 min
B) 3.8 min
C) 6.4 min
D) 7.7 min
E) 8.9 min

Question 65

In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?

A) 1.5 mm
B) 3.0 mm
C) 4.5 mm
D) 6.0 mm

Question 66

Using monochromatic light of 410 nm wavelength, a single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum. The same slit, when illuminated by a new monochromatic light source, produces a diffraction pattern with the second minimum at a 60.0° angle from the central maximum. What is the wavelength of this new light?

A) 276 nm
B) 293 nm
C) 309 nm
D) 326 nm
E) 342 nm

Question 67

A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10^-5 m wide, and then goes on to a screen that is 2.2 m from the slit. On the screen, how far is the second dark fringe from the center of the diffraction pattern?

A) 3.9 cm
B) 4.2 cm
C) 6.3 cm
D) 2.1 cm
E) 8.5 cm

Question 68

A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide. At what the angle away from the centerline does the second dark fringe occur?

A) 11.4°
B) 9.35°
C) 12.2°
D) 39.9°
E) 18.7°

Question 69

When a single slit that is 0.050 mm wide is illuminated by light of 550-nm wavelength, what is the angular separation between the first two minima on one side of the central maximum?

A) 0.36°
B) 0.47°
C) 0.54°
D) 0.63°
E) 1.3°

Question 70

Light of wavelength 687 nm passes through a single slit that is 0.75 mm wide. At what distance from the slit should a screen be placed so that the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the pattern?

A) 0.39 m
B) 0.93 m
C) 1.1 m
D) 1.5 m
E) 1.9 m

Question 71

Light of wavelength 580 nm is incident on a slit of width 0.30 mm. An observing screen is placed 2.0 m past the slit. Find the distance on the screen of the first order dark fringe from the center of the pattern.

A) 0.26 mm
B) 1.5 mm
C) 1.9 mm
D) 3.9 mm
E) 7.7 mm

Question 72

Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a frequency of 3.6 MHz. All radio measurements are made far from the antennas. What is the smallest angle, reckoned east of north from midway between the antennas, at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s)

A) 50°
B) 55°
C) 45°
D) 40°
E) 35°

Question 73

A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?

Question 74

A single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum. If monochromatic light of 530.0-nm wavelength is used for the illumination, what is the width of the slit?

A) 825 nm
B) 791 nm
C) 757 nm
D) 723 nm
E) 689 nm

Question 75

Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is viewed on a screen that is 1.5 m from the slit. What is the width on the screen of the central maximum?

A) 0.34 cm
B) 0.68 cm
C) 0.92 cm
D) 1.2 cm
E) 1.5 cm

Question 76

A single slit, 1400 nm wide, forms a diffraction pattern when illuminated by monochromatic light of 490-nm wavelength. What is the largest angle from the central maximum at which the intensity of the light is zero?

A) 44°
B) 41°
C) 38°
D) 35°
E) 32°

Question 77

When light of wavelength 450 nm falls on a single slit of width 0.30 mm, what is the angular width of the central bright region?

A) 0.086°
B) 0.13°
C) 0.17°
D) 0.26°
E) 0.35°

Question 78

At most, how many bright fringes can be formed on one side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a pair of slits that are apart?

A) 10
B) 9
C) 8
D) 11
E) 12

Question 79

Two radio antennas are 120 m apart on a north-south line. The two antennas radiate in phase at a frequency of 5.6 MHz. All radio measurements are made far from the antennas. What is the smallest angle, reckoned north of east from midway between the antennas, at which destructive interference of the two radio waves occurs? (c = 3.00 × 10⁸ m/s)

A) 13°
B) 6.4°
C) 9.7°
D) 16°
E) 19°

Question 80

A single thin slit forms a diffraction pattern when illuminated with monochromatic light. The fourth minimum of the pattern occurs at an angle of 32.0° away from the central maximum. At what angle does the fifth minimum occur?

A) 41.5°
B) 41.0°
C) 40.5°
D) 42.0°
E) 42.5°