Deck 35: Diffraction

Question 1

A single slit that is 2100 nm wide forms a diffraction pattern when illuminated by monochromatic light of 680-nm wavelength. At an angle of 10° from the central maximum, what is the ratio of the intensity to the intensity of the central maximum?

A) I/I₀ = 0.35
B) I/I₀ = 0.39
C) I/I₀ = 0.43
D) I/I₀ = 0.47
E) I/I₀ = 0.51

Answer 1

I/I₀ = 0.35

Question 2

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

Answer 2

762 nm

Question 3

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.

Answer 3

It becomes wider.

Question 4

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 5

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 6

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

A) 26.0°
B) 1.94°
C) 5.05°
D) 0.44°

Question 7

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 8

If the central maximum in a single slit diffraction pattern has intensity I₀, the intensity of the secondary maximum that is nearest to it is closest to

A) 0.045I₀.
B) I₀/4.
C) I₀/2.
D) I₀.
E) 2I₀.

Question 9

A slit of width 2.0 μm is used in a single slit experiment with light of wavelength 650 nm. If the intensity at the central maximum is I₀, what is the intensity 10° from the center?

A) 0.53I₀
B) 0.030I₀
C) 0.43I₀
D) 0.50I₀
E) 0.35I₀

Question 10

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 11

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 12

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 13

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 14

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 15

A thin beam of light of wavelength 625 nm goes through a thin slit and falls on a screen 3.00 m past the slit. You observe that the first completely dark fringes occur on the screen at distances of ±8.24 mm from the central bright fringe, and that the central bright fringe has an intensity of 2.00 W/m² at its center.
(a) How wide is the slit?
(b) What is the intensity of light at a point on the screen that is one-quarter of the way from the central bright fringe to the first dark fringe?

Question 16

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 17

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 18

If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged?

A) The resolving power quadruples.
B) The resolving power doubles.
C) The resolving power is reduced to 1/2 of its original value.
D) The resolving power is reduced to 1/4 of its original value.
E) The resolving power does not change unless the focal length changes.

Question 19

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 20

A lens is designed to work in the visible, near-infrared, and near-ultraviolet. The best resolution of this lens from a diffraction standpoint is

A) the same for all wavelengths.
B) in the near-ultraviolet.
C) in the visible.
D) in the near-infrared.
E) indeterminate.

Question 21

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 22

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

Question 23

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 24

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 25

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 26

Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes. What is the wavelength of the x-rays?

A) 0.14 nm
B) 0.17 nm
C) 0.21 nm
D) 0.24 nm
E) 0.27 nm

Question 27

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 28

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 29

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 30

A researcher is investigating a cubic crystal with x-rays. He is looking at Bragg reflection from the planes parallel to the cube faces. He finds that when using x-rays of 0.165 nm a strong first maximum occurs when the beam makes an angle of 23.5° with the planes. What is the spacing of adjacent atoms in the crystal?

Question 31

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 32

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 33

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 34

If an x-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference, at what angle will the second order line appear?

A) 40°
B) 20°
C) 43°
D) 4.0°
E) 11°

Question 35

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 36

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 37

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 38

If an x-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference, what is the plane spacing?

A) 0.28 nm
B) 0.070 nm
C) 0.32 nm
D) 0.16 nm
E) 0.14 nm

Question 39

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 40

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 41

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, the wavelength of the light is 600 nm, and index of refraction of the liquid in the eye is 1.34?

A) 0.42 mrad
B) 0.21 mrad
C) 0.14 mrad
D) 0.11 mrad
E) 0.26 mrad

Question 42

Light of wavelength 500 nm illuminates a round 0.50-mm diameter hole. A screen is placed 6.3 m behind the slit. What is the diameter of the central bright area on the screen?

A) 15 mm
B) 270 μm
C) 7.7 mm
D) 3800 μm

Question 43

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is 5.0 × 10^-4 rad and the person has excellent vision?

A) 1.3 km
B) 5.0 km
C) 4.8 km
D) 0.65 km
E) 2.6 km

Question 44

A radio telescope 200 m in diameter is used to investigate sources emitting a 21-cm wavelength wave. What is the minimum angular separation of the sources that can be resolved by this system?

A) 0.073°
B) 0.030°
C) 0.0013°
D) 0.154°
E) 0.0026°

Question 45

A certain astronomical telescope has a diameter of 5.60 m. Considering only the limitation due to diffraction, what is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A) 0.111 µrad
B) 0.311 µrad
C) 0.270 µrad
D) 0.135 µrad
E) 0.405 µrad

Question 46

Treat each of your eyes as a circular aperture of diameter 3.5 mm. Light of wavelength 500 nm is used to view two point sources that are 894 m distant from you. How far apart must these two point sources be if they are to be just resolved by your eye? Assume that the resolution is diffraction limited and use Rayleigh's criterion.

Question 47

Light of wavelength 633 nm from a He-Ne laser passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The diameter of the central bright area is 5.4 cm. What is the diameter of the aperture?

A) 110 μm
B) 2.0 μm
C) 6600 μm
D) 960 μm

Question 48

A camera used for aerial surveillance has a lens with a 30-cm maximum aperture and a 42-cm focal length. Assume light of 550-nm wavelength is used and that the resolution of the camera is limited solely by diffraction. What is the angular resolution of the camera at maximum aperture?

A) 1.6 µrad
B) 2.2 µrad
C) 3.2 µrad
D) 4.5 µrad
E) 6.3 µrad

Question 49

A 10-inch telescope (25.4 cm in diameter) is used to determine if what appears to be one star is actually two stars. Stars are so far away that they are essentially point sources. How close (in angle) can the two stars be and still be resolved by this telescope if it is focusing light of wavelength of 550 nm? (Consider only the limitation due to diffraction.)

A) 4.2 × 10^-8 degree
B) 2.6 × 10^-6 degree
C) 3.0 × 10^-4 degree
D) 1.5 × 10^-4 degree
E) 6.6 × 10^-8 degree