Deck 22: Wave Optics

Question 1

A double slit illuminated with light of wavelength 588 nm forms a diffraction pattern on a screen 11.0 cm away. The slit separation is 2464 nm. What is the distance between the third and fourth bright fringes away from the central fringe?

A) 23.9 cm
B) 5.96 cm
C) 5.59 cm
D) 2.63 cm

Answer 1

23.9 cm

Question 2

In a double-slit experiment, if the slit separation is increased, which of the following happens to the interference pattern shown on the screen?

A) The minima get closer together.
B) The maxima stay at the same position.
C) The minima and maxima stay at the same position.
D) The minima stay at the same position.
E) The maxima get further apart.

Answer 2

The minima get closer together.

Question 3

In a double slit experiment, if the separation between the two slits is 0.050 mm and the distance from the slits to a screen is 2.5 m, find the spacing between the first-order and second-order bright fringes when coherent light of wavelength 600 nm illuminates the slits.

A) 1.5 cm
B) 3.0 cm
C) 4.5 cm
D) 6.0 cm
E) 9.0 cm

Answer 3

3.0 cm

Question 4

A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the screen is 1.00 cm wide, as measured between the dark fringes that border it on either side. Which of the following actions would decrease the width of the central bright fringe? (There may be more than one correct choice.)

A) increase the wavelength of the light
B) decrease the wavelength of the light
C) increase the width of the slit
D) decrease the width of the slit
E) put the apparatus all under water

Question 5

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.

Question 6

At most, how many bright fringes can be formed on each side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a double slit whose spacing is 1.97 × 10^-6 m?

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

Question 7

Coherent monochromatic light of wavelength 632.8 nm passes through a pair of thin parallel slits. The figure shows the central portion of the pattern of bright fringes viewed on a screen 1.40 m beyond the slits. What is the distance between the two slits?

A) 0.0703 mm
B) 0.141 mm
C) 0.281 mm
D) 0.562 mm
E) 0.633 mm

Question 8

Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The m = 5 bright fringe of the unknown wavelength overlaps the
M = 4 bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?

A) 456 nm
B) 326 nm
C) 380 nm
D) 713 nm

Question 9

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?

A) It stays the same.
B) It becomes narrower.
C) It becomes wider.
D) Its behavior depends on the wavelength of the light.

Question 10

Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A woman is standing opposite the midpoint between the speakers and is initially 35.0 m from the midpoint. As she slowly walks parallel to the line connecting the speakers, at what angle θ (relative to the centerline coming outward from the midpoint between the speakers) will she first hear no sound?

A) 0.063°
B) 3.6°
C) 7.2°
D) 1.8°
E) 11°

Question 11

A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. Light waves arrive at the two slits in phase, and a fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 complete bright fringes per centimeter on the screen near the center of the pattern, what is the wavelength of the monochromatic light?

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

Question 12

In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits simultaneously. 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
E) 9.0 mm

Question 13

Light from a 600 nm source goes through two slits 0.080 mm apart. What is the angular separation of the two first order maxima occurring on a screen 2.0 m from the slits?

A) 0.15°
B) 0.86°
C) 0.015°
D) 0.0075°
E) 1.75°

Question 14

Light from a monochromatic source shines through a double slit onto a screen 5.00 m away. The slits are 0.180 mm apart. The dark bands on the screen are measured to be 1.70 cm apart. What is the wavelength of the incident light?

A) 457 nm
B) 306 nm
C) 392 nm
D) 612 nm
E) 784 nm

Question 15

In the two-slit experiment, monochromatic light of frequency 5.00 × 10¹⁴ Hz passes through a pair of slits separated by 2.20 × 10^-5 m. (c = 3.00 × 10⁸ m/s)
(a) At what angle away from the central bright spot does the third bright fringe past the central bright spot occur?
(b) At what angle does the second dark fringe occur?

Question 16

Light of wavelength 575 nm passes through a double-slit and the third order bright fringe is seen at an angle of 6.5° away from the central fringe. What is the separation between the double slits?

A) 5.0 µm
B) 10 µm
C) 15 µm
D) 20 µm
E) 25 µm

Question 17

Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s)

A) 43°
B) 22°
C) 68°
D) 47°
E) 30°

Question 18

Light of wavelength 519 nm passes through two slits. In the interference pattern on a screen 4.6 m away, adjacent bright fringes are separated by 5.2 mm in the general vicinity of the center of the pattern. What is the separation of the two slits?

Question 19

In a two-slit experiment, the slit separation is 3.00 × 10^-5 m. The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits. If the seventh bright fringe on the detector is 10.0 cm away from the central fringe, what is the wavelength of the light passing through the slits?

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

Question 20

In a double slit experiment, the slit separation is constructed to be exactly 4 times the wavelength of the light passing through the slits. At what angles from the center of the pattern will the third bright fringes on both sides of the central fringe occur?

A) ±48.6°
B) ±75.0°
C) ±67.5°
D) ±36.9°
E) ±43.0°

Question 21

When monochromatic light illuminates a grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?

A) 336 nm
B) 363 nm
C) 452 nm
D) 633 nm
E) 752 nm

Question 22

Light passes through a pair of very thin parallel slits. The resulting interference pattern is viewed far from the slits at various angles θ relative to the centerline coming outward from the midpoint between the slits. The central bright fringe is at θ = 0°. If the central bright fringe has intensity I₀, what is the intensity of the next bright fringe on either side of it?

A) I₀
B) I_0/
C) I₀/2
D) I₀ cos 15°
E) I₀ cos² 15°

Question 23

A single slit forms a diffraction pattern with monochromatic light. The 4th minimum of the pattern occurs at an angle of 35° from the central maximum. How many bright bands are on each side of the central maximum?

A) 5
B) 4
C) 6
D) 7
E) 8

Question 24

Monochromatic light is incident on a grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light?

A) 202 nm
B) 403 nm
C) 452 nm
D) 605 nm
E) 806 nm

Question 25

If the fifth order minimum in the diffraction pattern due to a thin slit is at 40° from the central maximum, at what angle does the first order minimum occur?

A) 8.0°
B) 3.4°
C) 4.0°
D) 7.4°
E) 1.7°

Question 26

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

A) 0.39 m
B) 0.47 m
C) 0.93 m
D) 1.1 m
E) 1.9 m

Question 27

A diffraction grating has 300 lines per mm. If light of frequency 4.76 × 10¹⁴ Hz is sent through this grating, at what angle does the first order maximum occur? (c = 3.00 × 10⁸ m/s)

A) 56°
B) 44°
C) 22°
D) 11°
E) 28°

Question 28

Monochromatic laser light of frequency 5.20 × 10¹⁴ Hz is shown on a pair of thin parallel slits, and the pattern is viewed on a screen 1.20 m away. The fifth bright fringes (not counting the central fringe) occur at ±2.12 cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent liquid. When the experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central bright fringe. (c = 3.00 × 10⁸ m/s)
(a) How far apart are the slits?
(b) What is the index of refraction of the liquid?

Question 29

A single slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum, using monochromatic light of 490-nm wavelength. What is the width of the slit?

A) 762 nm
B) 731 nm
C) 700 nm
D) 668 nm
E) 637 nm

Question 30

In a diffraction grating experiment, light of 600 nm wavelength produces a first-order maximum 0.350 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum 0.870 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source?

A) 479 nm
B) 497 nm
C) 567 nm
D) 749 nm
E) 794 nm

Question 31

In the figure, a slit 0.30 mm wide is illuminated by light of wavelength 426 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 diffraction minima on either side of the central diffraction maximum?

Question 32

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

A) 8
B) 2
C) 6
D) 5
E) 5.3

Question 33

Light of wavelength 525 nm passes through two slits separated by 0.500 mm and produces an interference pattern on a screen 7.80 m away. The intensity at the central maximum is I₀. What is the distance on the screen from the center of this central maximum to the point where the intensity due to double-slit interference has fallen to 1/2 I_0?

Question 34

A single slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum, when monochromatic light of 630-nm wavelength is used. The same slit, 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) 425 nm
B) 450 nm
C) 475 nm
D) 500 nm
E) 525 nm

Question 35

A single slit illuminated with a 500 nm light gives a diffraction pattern on a far screen. The 5^th minimum occurs at 7.00° away from the central maximum. At what angle does the 18^th minimum occur?

A) 26.0°
B) 1.94°
C) 5.05°
D) 0.44°

Question 36

If the fifth order minimum in the diffraction pattern of a thin slit is at 40° from the central maximum, what is the highest order minimum in the pattern?

A) 6
B) 11
C) 8
D) 7
E) 9

Question 37

A laser beam passes through a thin slit. When the pattern is viewed on a screen 1.25 m past the slit, you observe that the fifth-order dark fringes occur at ±2.41 cm from the central bright fringe. The entire experiment is now performed within a liquid, and you observe that each of the fifth-order dark fringes is 0.790 cm closer to the central fringe than it was in air. What is the index of refraction of this liquid?

A) 1.33
B) 1.40
C) 1.49
D) 1.62
E) 3.05

Question 38

A slit of width 0.010 mm has light of frequency 5.0 × 10¹⁴ Hz passing through it onto a screen 60 cm away. How wide is the central maximum? (c = 3.00 × 10⁸ m/s)

A) 0.12 cm
B) 7.2 cm
C) 1.8 cm
D) 3.6 cm
E) 0.90 cm

Question 39

In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m². What is the intensity halfway between the center of this fringe and the first dark band, assuming that the small-angle approximation is valid?

A) 6.2 µW/m²
B) 3.1 µW/m²
C) 4.7 µW/m²
D) 1.6 µW/m²
E) 0.12 µW/m²

Question 40

A single slit, which is 0.050 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?

A) 0.36°
B) 0.47°
C) 0.54°
D) 0.63°
E) 0.73°

Question 41

A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the microwave wavelength is 6.0 cm, what is the largest angle away from the central maximum at which an intensity maximum occurs.

A) 64°
B) 69°
C) 74°
D) 79°
E) 84°

Question 42

A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot. If the experiment were performed with all of the apparatus under water (which has an index of refraction of 1.33), what would be the TOTAL number of bright spots that would show up on the screen?

A) 6
B) 7
C) 12
D) 13
E) 14

Question 43

An 18-mm wide diffraction grating has rulings of 880 lines per mm. Monochromatic light of 590 nm wavelength is incident normally on the grating. What is the largest angle, measured from the central bright spot, at which an intensity maximum is formed?

A) 31°
B) 29°
C) 27°
D) 25°
E) 23°

Question 44

A diffraction grating is to be used to find the wavelength of the light in the emission spectrum of a gas. The grating spacing is not known, but a light having a known wavelength of 632.8 nm is deflected by 43.2° away from the central maximum in the second order by this grating. Light of the wavelength to be measured is deflected by 48.2° away from the central maximum in the second order. What is the wavelength of this light?

Question 45

A diffraction grating has rulings of 890 lines/mm. When white light is incident normally on the grating, what is the longest wavelength that forms an intensity maximum in the fifth order?

A) 225 nm
B) 200 nm
C) 250 nm
D) 275 nm
E) 300 nm

Question 46

Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32.0° from the central spot, how many TOTAL number of maxima can be seen?

A) 5
B) 7
C) 10
D) 11
E) 13

Question 47

A He-Ne laser, which produces light of wavelength 632.8 nm, is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5° from the central spot, what is the distance between the slits of the grating?

A) 0.905 µm
B) 1.81 µm
C) 2.20 µm
D) 3.62 µm
E) 4.52 µm

Question 48

What is the angular separation of the two second-order spectral lines having wavelengths 417 nm and 388 nm using a diffraction grating having 456 lines/mm?

A) 1.63°
B) 1.52°
C) 0.815°
D) 3.26°

Question 49

A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. What is the smallest microwave frequency for which only the central maximum occurs?
(c = 3.00 × 10⁸ m/s)

A) 0.50 GHz
B) 0.70 GHz
C) 1.0 GHz
D) 1.5 GHz
E) 2.0 GHz

Question 50

A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot. What is the TOTAL number of bright fringes that will show up on the screen?

A) 4
B) 5
C) 8
D) 9
E) 10

Question 51

A diffraction grating has 450 lines per mm. What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?

A) m = 2
B) m = 3
C) m = 4
D) m = 5
E) m = 6