Deck 35: Diffraction and Interference

Question 1

Two slits are illuminated with red light (λ = 650 nm). The slits are 0.25 mm apart and the distance to the screen is 1.25 m. What fraction of the maximum intensity on the screen is the intensity measured at a distance 3.0 mm from the central maximum?

A)0.94
B)0.92
C)0.96
D)0.98
E)0.99

Answer 1

0.94

Question 2

A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. S₁ and S₂ are in phase. The black circles are one and two wavelengths from their respective sources. The lighter circles are one-half and one-and-a-half wavelengths distant from their respective sources. If the waves shown arriving at P₁ both arrive with amplitude A, the resultant amplitude at point P₁ is ​ ​

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

Answer 2

2A.

Question 3

In a double-slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 100 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point 5 mm from the central maximum when the wavelength is 400 nm? (Convert your result so the angle is between 0 and 360°.)

A)90°
B)180°
C)270°
D)360°
E)160°

Answer 3

180°

Question 4

The bright and dark bands you see in a photograph of a double-slit interference pattern represent

A)the respective positions of the crests and the troughs of the light wave.
B)an interference pattern that is not present unless it is produced by the camera lens.
C)the respective positions of constructive and destructive interference of light from the two sources.
D)the respective positions of destructive and constructive interference of light from the two sources.
E)the respective positions of bright and dark particles of light.

Question 5

A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. S₁ and S₂ are in phase. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. If the waves shown arriving at P₂ both arrive with amplitude A, the resultant amplitude at point P₂ is

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

Question 6

Two slits are illuminated with green light (λ = 540 nm). The slits are 0.05 mm apart and the distance to the screen is 1.5 m. At what distance (in mm) from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum?

A)1
B)3
C)2
D)4
E)0.4

Question 7

Two slits separated by 0.10 mm are illuminated with green light (λ = 540 nm). Calculate the distance (in cm) from the central bright-region to the fifth bright band if the screen is 1.0 m away.

A)2.3
B)2.5
C)2.7
D)2.1
E)2.0

Question 8

For small angle approximations

A)the angle must be 10° or less
B)the angle must be 10 radians or less
C)the angle must be 1° or less
D)the angle must be 1 radian or less
E)the angle must be 45° or less

Question 9

Light is incident on a double-slit. The fourth bright band has an angular distance of 7.0° from the central maximum. What is the distance between the slits (in μm)? (Assume the frequency of the light is 5.4 × 1014 Hz.)

A)27
B)21
C)24
D)18
E)14

Question 10

In an interference pattern, the wavelength and frequency are

A)the same in both the regions of constructive interference and the regions of destructive interference.
B)greater in regions of constructive interference than in regions of destructive interference.
C)smaller in regions of constructive interference than in regions of destructive interference.
D)unchanged in regions of destructive interference but greater in regions of constructive interference.
E)unchanged in regions of destructive interference but smaller in regions of constructive interference.

Question 11

Estimate the distance (in cm) between the central bright region and the third dark fringe on a screen 5.00 m from two double slits 0.500 mm apart illuminated by 500-nm light.

A)3.47
B)2.15
C)1.75
D)1.50
E)1.25

Question 12

In a double-slit experiment, the distance between the slits is 0.2 mm, and the distance to the screen is 150 cm. What wavelength (in nm) is needed to have the intensity at a point 1 mm from the central maximum on the screen be 80% of the maximum intensity?

A)900
B)700
C)500
D)300
E)600

Question 13

A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. The black circles are one and two wavelengths from their respective sources. The lighter circles are one-half and one-and-a-half wavelengths distant from their respective sources. If the phase at S₁ and S₂ is zero at this instant, and the waves shown arriving at P₂ both arrive with amplitude A, the difference in phase angle at point P₂ (in radians) is ​ ​

A)0.
B)π/2.
C)π.
D)3π/2.
E)2π.

Question 14

In a double-slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 150 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point P when the angular distance of P is 10° relative to the central peak, and the wavelength is 500 nm? (Convert your result so the angle is between 0 and 360°.)

A)145°
B)155°
C)165°
D)135°
E)95°

Question 15

The electric fields arriving at a point P from three coherent sources are described by E₁ = E₀ sin ωt, E₂ = E₀ sin (ωt + π/4) and E₃ = E₀ sin (ωt + π/2). Assume the resultant field is represented by Ep = ER sin (ωt + α). The amplitude of the resultant wave at P is

A)E₀.
B)1.5E₀.
C)1.7E₀.
D)2.4E₀.
E)2.9E₀.

Question 16

The figure shows two point sources of light, A and B. B emits light waves that are +π radians out of phase with the waves from A. A is 3λ from P. B is 5λ from P. (λ is the wavelength.) The phase difference between waves arriving at P from A and B is

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

Question 17

A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. If the phase at S₁ and S₂ is zero at this instant, and the waves shown arriving at P₁ both arrive with amplitude A, the magnitude of the phase angle of each wave at point P₁ (in radians) is

A)0.
B)π.
C)2π.
D)3π.
E)π/2.

Question 18

The figure shows two point sources of light, A and B, that emit light waves in phase with each other. A is a distance of 3λ from point P. B is distant 5λ from P. (λ is the wavelength.) The phase difference between the waves arriving at P from A and B is ​ ​

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

Question 19

A laser beam (λ = 694 nm) is incident on two slits 0.100 mm apart. Approximately how far apart (in m) will the bright interference fringes be on the screen 5.00 m from the double slits?

A)3.47 × 10−3
B)3.47 × 10−2
C)3.47 × 10−4
D)3.47 × 10−6
E)3.47 × 10−5

Question 20

Two slits separated by 0.050 mm are illuminated with green light (λ = 540 nm). How many bands of bright lines are there between the central maximum and the 12-cm position? (The distance between the double slits and the screen is 1.0 m.)

A)1111
B)111
C)11
D)1
E)11111

Question 21

When you look at a single-slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the wavelength of the light is increased,

A)the pattern shrinks in size (central maximum less wide; other maxima in closer to it).
B)the pattern increases in size (central maximum wider; other maxima farther from it).
C)it does not affect the size of the pattern.
D)the width of the central maximum increases, but the other maxima do not change in position or width.
E)the width of the central maximum decreases, but the other maxima do not change in position or width.

Question 22

The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. In each figure the spacing d between the slits is the same. Which figure(s) represent(s) slits illuminated with light of the shortest wavelength λ? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 23

Which of the patterns shown below would appear on a screen when monochromatic light first passes through a narrow slit for which a = λ and then strikes the screen? Note that the darkest area in each illustration represents the brightest area on the screen.

A)
B)
C)
D)
E)

Question 24

A slit of variable width illuminated by light of wavelength λ is widened until the first order diffraction minimum moves out to a distance infinitely far away from the brightest location in the central maximum. In terms of the wavelength, the width of the slit is then

A)0.
B) .
C)λ.
D) .
E)2λ.

Question 25

How wide must a narrow slit be if the first diffraction minimum occurs at ±12° with laser light of 633 nm?

A)3.0 × 10−6 m
B)3.0 × 10−5 m
C)6.1 × 10−6 m
D)6 .1× 10−5 m
E)1.5 × 10−6 m

Question 26

The pupil of a cat's eye narrows to a slit width of 0.5 mm in daylight. What is the angular resolution of the cat's eye in daylight (λ = 500 nm)?

A)0.01 rads
B)10−5 rads
C)10−3 rads
D)10−4 rads
E)0.1 rads

Question 27

The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. Which figure(s) represent(s) slits with the greatest spacing d between the slits? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 28

A narrow slit is illuminated with sodium yellow light of wavelength 589 nm. If the central maximum extends to ±30.0°, how wide is the slit?

A)0.500 mm
B)2.20 × 10−6 m
C)3.33 × 10−5 m
D)1.18 μm
E)5.89 μm

Question 29

The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. In each figure the spacing d between the slits is the same. Which figure(s) represent(s) slits illuminated with light of the greatest wavelength λ? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 30

Plane waves of ultrasound, f = 51.0 kHz, impinge on a flat plane with a 1.00-cm-wide slit. What is the total angular width (2θ) of diffracted sound waves when the speed of sound in air is 340 m/s.

A)167°
B)83.6°
C)19.5°
D)41.8°
E)0.11°

Question 31

When you look at a single-slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the width of the slit is increased,

A)the pattern shrinks in size (central maximum less wide; other maxima in closer to it).
B)the pattern increases in size (central maximum wider; other maxima farther from it).
C)it does not affect the size of the pattern.
D)the width of the central maximum increases, but the other maxima do not change in position or width.
E)the width of the central maximum decreases, but the other maxima do not change in position or width.

Question 32

When a central dark fringe is observed in reflection in a circular interference pattern, waves reflected from the upper and lower surfaces of the medium must have a phase difference, in radians, of

A)0.
B)π/2.
C)π.
D)3π/2.
E)2π.

Question 33

The centers of two slits of width a are a distance d apart. If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light of wavelength λ, the ratio a/d is equal to

A)0.
B) .
C) .
D) .
E) .

Question 34

The superposition of two waves E1 = E0 sin(ωt) and E2 = E0 sin(ωt + φ) arriving at the same point in space at the same time is E =

A) .
B)2E0 sin(ωt)cos(φ).
C) .
D) .
E) .

Question 35

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. The number of fringes per unit length on the screen can be doubled

A)if the distance between the slits is doubled.
B)if the wavelength is changed to .
C)if the distance between the slits is quadruple the original distance and the wavelength is changed to .
D)if any of the above occurs.
E)only if the width of the slits is changed to .

Question 36

Helium-neon laser light (λ = 6.33 × 10−7 m) is sent through a 0.30-mm-wide single slit. What is the width of the central maximum on a screen 1.0 m from the slit?

A)2.0 cm
B)4.2 mm
C)1.1 cm
D)2.0 mm
E)0.70 mm

Question 37

Ray says that interference effects cannot be observed with visible light because random phase changes occur in time intervals less than a nanosecond. Stacy says that doesn't matter if collimated light from a single source reaches multiple openings. (They are arguing about a light source 50.0 cm away from two 0.0100-mm-wide slits, 2.00 mm apart, with a screen 1.00 m away from the slits.) Which one, if either, is correct, and why?

A)Ray, because the phases at the two slits will be random and different.
B)Ray, because it takes light over 3 ns to travel 1.00 m to the screen.
C)Stacy, because the difference in time of travel from the source to the slits is no more than about 7 × 10−12 s.
D)Stacy, but only if a lens is placed in front of the slits.
E)Both, because interference of light never occurs outside a physics lab.

Question 38

The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. Which figure(s) represent(s) slits with the smallest spacing d between the slits? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 39

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. The number of fringes per unit length on the screen can be halved

A)if the distance between the slits is changed to .
B)if the wavelength is changed to .
C)if the distance between the slits is the wavelength is changed to .
D)if any of the above occurs.
E)only if the width of the slits is changed to .

Question 40

When you look at a single-slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the width of the slit is decreased,

A)the pattern shrinks in size (central maximum less wide; other maxima in closer to it).
B)the pattern increases in size (central maximum wider; other maxima farther from it).
C)it does not affect the size of the pattern.
D)the width of the central maximum increases, but the other maxima do not change in position or width.
E)the width of the central maximum decreases, but the other maxima do not change in position or width.

Question 41

Light from a helium-neon laser (λ = 632.8 nm) is incident upon a 0.200-mm-wide slit. Find the total width of the central maximum 2.00 m from the slit.

Question 42

A single slit of width a is illuminated by light of wavelength λ. If a = 4.3λ, the maximum number of dark fringes on a semi-circular screen surrounding the slit is

A)2.
B)4.
C)6.
D)8.
E)9.

Question 43

Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case is the slit illuminated with light of the longest wavelength?

A)
B)
C)
D)
E)

Question 44

Each pattern shown below would appear on a screen when monochromatic light of wavelength λ first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case does the slit have the greatest width?

A)
B)
C)
D)
E)

Question 45

When you look through a sheer curtain at a distant street lamp, you see a pattern of colored spots of light. This occurs by

A)polarization of light in scattering and partial absorption by the threads.
B)interference of light waves that pass through the threads with light waves that pass through the openings between the threads.
C)refraction of light waves differentially in the cylindrical threads.
D)diffraction of light waves passing through the two dimensional pattern of openings between the threads.
E)reflection of light waves by the sides of the threads.

Question 46

Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case is the slit illuminated with light of the shortest wavelength?

A)
B)
C)
D)
E)

Question 47

Scattered light in the atmosphere is often partially polarized. The best way to determine whether or not light from a particular direction in the sky shows polarization is to

A)diffract the light through a single slit.
B)squint while looking in that direction.
C)rotate a piece of polaroid film about an axis parallel to the ray while looking through it in that sky direction.
D)rotate a piece of polaroid film about an axis perpendicular to the ray while looking through it in that sky direction.
E)reflect the rays from that direction on a shiny metal surface.

Question 48

Each pattern shown below would appear on a screen when monochromatic light of wavelength λ first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case does the slit have the narrowest width?

A)
B)
C)
D)
E)