Deck 25: Interference and Diffraction

Question 1

What minimum thickness of oil (n = 1.50) on the surface of water (n = 1.33) would give destructive interference for 550 nm light at normal incidence?

A) 275 nm
B) 183 nm
C) 92.0 nm
D) 80.0 nm
E) 78.0 nm

Answer 1

183 nm

Question 2

Two coherent sources emit waves of wavelength 2.0 m in phase. If the difference in path lengths to an observer is 7.0 m, what kind of interference occurs?

A) no interference occurs
B) neither constructive nor destructive, but something in between
C) constructive
D) destructive

Answer 2

destructive

Question 3

A thin film of soapy water (n = 1.37) is held vertical. Light of wavelength 600 nm is reflected from the film and horizontal dark lines appear. What is the difference in thickness of the soap film from one band to the next?

A) 600 nm
B) 438 nm
C) 300 nm
D) 219 nm
E) 900 nm

Answer 3

219 nm

Question 4

A general condition for two coherent waves to undergo constructive interference is that

A) their phase difference is zero.
B) their phase difference is π/2 rad.
C) their phase difference is ±π/2 rad.
D) their phase difference is an even integral multiple of π rad.
E) their phase difference is an odd integral multiple of π rad.

Question 5

Two coherent waves, each with amplitude A, are in phase as they overlap in a region of space. The amplitude of the superposed wave is

A) 0.
B) A.
C) 2A.
D) 3A.
E) 4A.

Question 6

Two coherent waves, each with intensity I₀, are in phase as they overlap in a region of space. The intensity of the superposed wave is

A) 0.
B) I_0.
C) 2I_0.
D) 3I_0.
E) 4I_0.

Question 7

A thin film of soapy water (n = 1.37) is held vertical. Light of wavelength 600 nm is reflected from the film and horizontal dark lines appear. What is the thinnest soap film for which a bright band will occur?

A) 150 nm
B) 109 nm
C) 90.0 nm
D) 438 nm
E) 219 nm

Question 8

What is the smallest thickness of a coating of magnesium fluoride (n = 1.38) applied to glass (n = 1.50) that gives minimum reflection for 600 nm light?

A) 600 nm
B) 300 nm
C) 435 nm
D) 109 nm
E) 100 nm

Question 9

Two coherent waves interfere constructively. One wave has amplitude 8A₀ and the other has amplitude 6A₀. The amplitude of the superposed wave is

A) 6A_0.
B) 8A_0.
C) 10A_0.
D) 14A_0.
E) 2A_0.

Question 10

A thin film of magnesium fluoride (n = 1.38) is applied to glass (n = 1.50). If the thickness of the film is 100 nm, for what visible wavelength will it be nonreflecting?

A) 600 nm
B) 578 nm
C) 552 nm
D) 504 nm
E) 491 nm

Question 11

If two coherent waves, one with intensity 8.0 I₀ and the other with intensity 4.0 I₀, undergo destructive interference, what is the resulting intensity?

A) 4.0 I₀
B) 6.0 I₀
C) −4.0 I₀
D) 1.9 I₀
E) 0.69 I₀

Question 12

Wave 1 has amplitude of 9.0 A₀ and wave 2 has amplitude 4.0 A₀. What is the ratio of their intensities, I₁/I₂?

A) 20
B) 5.1
C) 2.3
D) 1.5
E) 1.3

Question 13

A Michelson interferometer is set up for microwaves. Initially the reflectors are placed so the detector reads a maximum. When one of the reflectors is moved 12 cm, the reading goes from a maximum to a minimum and back to maximum six times. What is the wavelength of the microwaves?

A) 0.5 cm
B) 4 cm
C) 1 cm
D) 2 cm

Question 14

Using a Michelson interferometer and a light source of 400 nm, a change from bright to dark indicates a change in the difference of arm lengths of

A) 2.0 × 10^-4 mm.
B) 4.0 × 10^-4 mm.
C) 3.0 × 10^-4 mm.
D) 1.0 × 10^-4 mm.

Question 15

What is the minimum thickness of the air layer between two flat glass surfaces if the glass is to appear bright when 450 nm light is incident normally?

A) 57.0 nm
B) 113 nm
C) 170 nm
D) 226 nm

Question 16

Coherent light of a single frequency passes through a double slit with a separation d, to produce a pattern on a screen a distance D from the slits. What would cause the separation between adjacent minima on the screen to increase?

A) increase the index of refraction of the medium in which the setup is immersed
B) increase the separation d between the slits
C) increase the distance D
D) increase the frequency of the incident light

Question 17

A general condition for two coherent waves to undergo destructive interference is that

A) their phase difference is zero.
B) their phase difference is π/2 rad.
C) their phase difference is ±π/2 rad.
D) their phase difference is an even integral multiple of π rad.
E) their phase difference is an odd integral multiple of π rad.

Question 18

What minimum thickness of oil (n = 1.50) on the surface of water (n = 1.33) would give constructive interference for 550 nm light at normal incidence?

A) 78.0 nm
B) 80.0 nm
C) 92.0 nm
D) 183 nm
E) 275 nm

Question 19

Two coherent waves interfere constructively. One wave has an intensity of 8.00 I₀ and the other has an intensity of 4.00 I₀. What is the intensity of the superposed wave?

A) 4.00 I₀
B) 8.00 I₀
C) 12.0 I₀
D) 23.3 I₀
E) 24.0 I₀

Question 20

Wave 1 has intensity 9.0 I₀ while wave 2 has intensity 4.0 I₀. What is their ratio of amplitudes, A₁/A₂?

A) 20
B) 5.1
C) 2.3
D) 1.5
E) 1.3

Question 21

Laser light of 589 nm wavelength is shone through parallel slits forming a series of maxima on a screen 4.20 m away. If the distance between the central maximum and the first-order maximum is 1.67 cm, what is the slit separation?

A) 3.90 × 10^-3 cm
B) 3.98 × 10^-3 m
C) 9.98 × 10^-5 m
D) 1.40 × 10^-3 m
E) 1.48 × 10^-4 m

Question 22

If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm, what angle separates the two fourth-order maxima?

A) 0.768°
B) 3.07°
C) 0.307°
D) 1.54°
E) 0.154°

Question 23

Substituting tan θ for sin θ results in what percent error for an angle of 5.00°?

A) 5.00
B) 0.0166
C) 0.0333
D) 0.191
E) 0.382

Question 24

For an angle of 10 degrees, what is the percent difference between sin θ and θ in radians?

A) 0.1%
B) 0.3%
C) 0.5%
D) 0.7%
E) more than 1%

Question 25

In a double-slit experiment, when both interference and diffraction are taken into account, which is the lowest order maximum that is missing in the case where the slit separation is 0.020 mm and the slit widths are each 0.005 mm?

A) 1
B) 2
C) 3
D) 4
E) no order is missing

Question 26

In a double-slit interference pattern, the third maximum from the central maximum corresponds to which value of m?

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

Question 27

A Young's double-slit experiment is performed and then repeated after moving the screen to three times the previous distance from the slits. What happens to the angular separation (as measured from the slits) of the fourth-order maxima?

A) There is no change.
B) It becomes one-third the original value.
C) It becomes four times the original value.
D) It triples.
E) It increases by a factor of 2.25.

Question 28

A laser beam is directed through a grating and a first-order maximum is produced at 17°. What is the highest order maximum that can be produced by this arrangement?

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

Question 29

Using a double slit with d = 300 nm and light of wavelength 400 nm, what would you see on a distant screen?

A) The intensity is maximum at the center and gradually decreases to either side.
B) The intensity is minimal at the center and gradually increases to either side.
C) The intensity is maximum in a single narrow line at the center.
D) The intensity is minimal in a single narrow line at the center.

Question 30

If the two second-order maxima (m = ±2) are separated by 2.0 cm on the screen in a double-slit experiment, what is the separation of the m = ±3 maxima? Assume the angles are very small.

A) 1.5 cm
B) 2.0 cm
C) 2.5 cm
D) 3.0 cm
E) 3.5 cm

Question 31

For an angle of one degree, to how many significant figures do sin θ and θ (in radians) agree?

A) 3
B) 4
C) 5
D) 6
E) 7

Question 32

Light of wavelength 450 nm produces a first-order maximum at 27° when viewed through a grating. At what angle would a first-order maximum occur for a wavelength of 600 nm viewed through this grating?

A) 54°
B) 40°
C) 36°
D) 37°
E) 14°

Question 33

Increasing the wavelength in a double-slit experiment has what effect on the position of the maxima on a screen at fixed distance?

A) none
B) maxima get closer together
C) maxima get farther apart
D) maxima get cancelled by minima
E) maxima pass minima on the screen

Question 34

What is the highest order maximum possible using a grating with 600 slits per mm for a wavelength of 700 nm?

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

Question 35

A laser beam passes through a grating and produces a first-order maximum at an angle of 25°. At what angle is the second-order maximum?

A) 75°
B) 58°
C) 50°
D) 35°
E) 27°

Question 36

What slit separation is required for a grating to produce a first-order maximum at an angle of 40.0° for a wavelength of 589 nm?

A) 109 nm
B) 690 nm
C) 378 nm
D) 458 nm
E) 916 nm

Question 37

A double-slit experiment is performed and then redone using slits of double the previous separation. Nothing else is changed. If the approximation sin θ ≈ θ holds, what happens to the angle between the maxima?

A) it stays the same
B) it doubles
C) it quadruples
D) it halves
E) it quarters

Question 38

In a double-slit experiment, the intensity of the light reaching the center of the screen from one slit alone is I0 and intensity of the light reaching the center from the other slit alone is 9I0. When both slits are open, what is the intensity of the light at the minima nearest the center?

A) 4I₀
B) 0
C) 8I₀
D) 2I₀

Question 39

In a Young's double-slit experiment, a fifth-order maximum occurs at an angle of 1.422°. If the screen is 3.90 m from the slits and the slit separation is 0.135 mm, what wavelength is being used?

A) 335 nm
B) 670 nm
C) 476 nm
D) 589 nm
E) 690 nm

Question 40

A grating is made with 600 slits per millimeter. What is the slit separation?

A) 600 nm
B) 1.67 × 10^-6 m
C) 3.33 × 10^-6 m
D) 160 pm
E) 916 nm

Question 41

Huygens's principle only applies to

A) electromagnetic waves.
B) water waves.
C) sound waves.
D) all of these choices are correct

Question 42

A single slit of width 0.030 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What is the width of the central maximum?

A) 1.7 cm
B) 3.3 cm
C) 6.7 cm
D) 1.5 mm
E) 3.0 mm

Question 43

The resolution of a microscope can be most improved by

A) increasing the wavelength and the diameter of the lens.
B) decreasing the wavelength and the diameter of the lens.
C) decreasing the wavelength and increasing the diameter of the lens.
D) increasing the wavelength and decreasing the diameter of the lens.

Question 44

Two point sources of light of wavelength 600 nm are being viewed by a telescope with aperture width 2.0 cm. What is the smallest angular separation at which the two sources can be resolved?

A) 7.3 × 10^-5 rad
B) 3.7 × 10^-5 rad
C) 7.3 × 10^-5 deg
D) 3.7 × 10^-5 deg
E) 4.2 × 10^-3 deg

Question 45

X-rays of wavelength 0.080 nm are used in a Bragg scattering experiment with a crystal. If the first-order maximum is found at an incident angle of 6.0° relative to the crystal surface, what is the plane spacing in the crystal?

A) 0.31 nm
B) 0.71 nm
C) 1.4 nm
D) 0.38 nm
E) 0.77 nm

Question 46

How far away can two point sources of light of wavelength 500 nm be, if they are just resolvable in a telescope with an aperture width of 1.5 cm?

A) 25 km
B) 12 km
C) 90 m
D) 12 m
E) more information is needed

Question 47

A grating with 8000 slits over 2.54 cm is illuminated by light of a wavelength of 546 nm. What is the angle for the third-order maximum?

A) 31.1°
B) 15.1°
C) 26.3°
D) 10.5°

Question 48

When light of wavelength 700 nm is used in a single-slit diffraction pattern, the central maximum has a width of 3.5 cm. When the light source is replaced by one of wavelength 500 nm, what central width will result? Assume small angles.

A) 3.5 cm
B) 3.0 cm
C) 2.5 cm
D) 4.9 cm
E) 4.0 cm

Question 49

If the eye can resolve points separated by 2.2 × 10^-4 rad, how many dpi ensure you don't see individual dots when viewing something 12 inches away? (dpi = dots per inch)

A) 250
B) 340
C) 380
D) 400
E) 590

Question 50

Max von Laue is known for his work with

A) double-slit interference.
B) single-slit diffraction.
C) x-ray crystallography.
D) holography.
E) magnetic resonance imaging.

Question 51

Holograms appear three-dimensional because

A) they are in color.
B) they are transparent.
C) they consist of Young double slits.
D) they recreate wavefronts as if they were coming from the original source.
E) of their spectral response to refraction.

Question 52

In an x-ray diffraction experiment, x-rays of fixed wavelength yield a first-order maximum at an incident angle of 12° relative to the surface. At what angle would one expect to find the corresponding third-order maximum?

A) 4.0°
B) 12°
C) 36°
D) 39°
E) more information is needed

Question 53

A single slit of width 0.0300 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What angle does the central maximum subtend as measured from the slit?

A) 1.91°
B) 3.82°
C) 0.945°
D) 1.50°
E) 3.00°

Question 54

When the slit width is doubled, what happens to the width of the central maximum in a single-slit diffraction pattern? Assume small angles.

A) nothing
B) it doubles
C) it halves
D) it quadruples
E) it quarters

Question 55

What is the angular resolution of the eye at a wavelength of 500 nm for a pupil diameter of 2.8 mm?

A) 1.8 × 10^-4 rad
B) 2.2 × 10^-4 rad
C) 8.9 × 10^-5 rad
D) 4.5 × 10^-5 rad
E) 3.3 × 10^-5 rad

Question 56

Holography was invented by

A) Max von Laue.
B) Sir David Brewster.
C) Rosalind Franklin.
D) Dennis Gabor.
E) Bill Gates.

Question 57

In a single-slit experiment, light of wavelength 500 nm is used to produce a diffraction pattern on a screen 4.0 m away. If the distance between both third-order minima is 6.0 cm, what is the slit width?

A) 2.0 × 10^-4 m
B) 1.0 × 10^-4 m
C) 4.0 × 10^-4 m
D) 0.67 × 10^-4 m
E) 0.44 × 10^-4 m

Question 58

If a laser printer prints at 600 dots per inch, what is the angular separation of the dots when viewed from 40 cm?

A) 4.2 × 10^-5 rad
B) 2.7 × 10^-4 rad
C) 1.1 × 10^-4 rad
D) 5.5 × 10^-8 rad
E) 3.7 × 10^-3 rad

Question 59

What is the limiting angle of resolution, in degrees, for a microscope with an objective 0.50 cm in diameter when viewing with light of wavelength 590 nm?

A) 2.1 × 10^-3
B) 4.1 × 10^-3
C) 7.2 × 10^-5
D) 8.2 × 10^-3
E) 1.4 × 10^-4

Question 60

For a coherent plane wave approaching an obstacle with a rectangular opening, diffraction becomes significant under which of the following circumstances?

A) both dimensions of the rectangular opening are comparable to the wavelength
B) one or more dimensions of the rectangular opening are comparable to the wavelength
C) both dimensions of the rectangular opening are larger than the wavelength
D) only if the opening is circular

Question 61

In a two-slit experiment, there are 11 bright fringes within the central diffraction maximum (on each side, the first diffraction minimum coincides with where the next interference bright fringe would be). What is the ratio of the slit width to the slit separation?

A) 5
B) 1/6
C) 1/5
D) 6

Question 62

Two planes of atoms in a crystal are separated by 3.25 × 10^-10 m. How many maxima will there be in the diffraction pattern for x-rays of wavelength 2.0 × 10^-10 m scattered from this crystal?

A) 4
B) 2
C) 3
D) an infinite number
E) 1

Question 63

A canvas tent has a single, tiny hole in its side. While inside the tent, you observe a dot on the wall of the tent, which is 2.0 m away (the dot is due to a distant point source of light of wavelength 550 nm). The dot has a diameter of 2.0 mm, and there is a faint ring around it. What is the size of the hole in the tent?

A) 0.55 mm
B) 0.67 mm
C) 1.10 mm
D) 1.34 mm

Question 64

Two planes of atoms in a crystal are separated by 3.25 × 10^-10 m. Light of what wavelength would show constructive interference at an angle of 17.5 degrees relative to the crystal surface?

A) 3.9 × 10^-10 m
B) 4.9 × 10^-9 m
C) 9.75 × 10^-10 m
D) 1.46 × 10^-10 m
E) 1.95 × 10^-10 m

Question 65

When scattering 0.328 nm x-rays off a crystal, the first interference maximum occurs at an angle of 23.0 degrees relative to the crystal surface. At what angle does the second maximum occur?

A) 51.4°
B) 46.0°
C) 34.5°
D) There is no second maximum.

Question 66

Light is shone through an adjustable-width slit in an otherwise opaque barrier, and a diffraction pattern is observed. If the slit is decreased to half its original size, by what factor does the width of the central diffraction maximum change?

A) Decreases by a factor of four
B) Doubles
C) Halves
D) Increases four times

Question 67

If the distance between the slits in a double-slit apparatus is increased, while the width of each slit is kept the same, the number of interference fringes within the central diffraction maximum will

A) decrease.
B) increase.
C) remain the same.
D) may do any of the above.

Question 68

A Michelson interferometer is used to measure the index of refraction of a gas by counting interference fringes as the gas is slowly leaked into a transparent vessel placed in one arm of the interferometer. The vessel initially contains a vacuum, and as the gas is let in, 397 bright fringes are counted. That is, the central region of the screen changes from bright to dark and back to bright 397 times. If the wavelength of light used is 560 nm, and the vessel containing the gas is 25.0 cm long, what is the index of refraction of the gas?

A) 1.000111
B) 1.000222
C) 1.000445
D) 1.000889
E) 1.00178

Question 69

When scattering x-rays with a wavelength of 3.28 × 10^-10 m from a crystal, the first interference maximum occurs at an angle of 23.0 degrees relative to the crystal surface. What is the crystal spacing?

A) 4.2 × 10^-10 m
B) 16.8 × 10^-10 m
C) 6.3 × 10^-10 m
D) 8.4 × 10^-10 m

Question 70

Light from a HeNe laser (632.8 nm wavelength) is directed upon a straightened strand of human hair, 7.5 m from the wall. By examining the diffraction pattern produced on the wall, the diameter of the hair can be determined (the diffraction pattern thus produced has minima in the same locations as if the hair were a slit of the same width in an otherwise opaque barrier). If the central diffraction maximum is measured to be 14.6 cm wide, what is the diameter of the hair?

A) 65 µm
B) 32.5 µm
C) 43.3 µm
D) 86.6 µm

Question 71

A two-slit apparatus is illuminated with red light of wavelength 660 nm, and 9 interference maxima are observed within the 4.5 cm-wide central diffraction maximum on a distant screen. If blue light of wavelength 440 nm is used instead, how many fringes will there be in the new central diffraction maximum?

A) 3
B) 13
C) 9
D) 6

Question 72

What kind of image does a holographic plate produce for the viewer?

A) real
B) virtual
C) may be either virtual or real