Deck 37: Wave Optics

Question 1

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

Answer 1

11

Question 2

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

Answer 2

1.25

Question 3

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 3

0.94

Question 4

A thin sheet of plastic (n = 1.60) is inserted between two panes of glass to reduce infrared (λ = 700 nm) losses. What thickness (in nm) is necessary to produce constructive interference in the reflected infrared radiation?

A) 218
B) 109
C) 55
D) 318
E) 443

Question 5

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.40). What is the wavelength of the light (in nm) in the bubble film?

A) 255
B) 500
C) 700
D) 357
E) 422

Question 6

The figure shows two point sources of light, A and B, that emit light waves in phase with each other. A is distant 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 7

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 50 mm thick. What is the change of phase of the light reflected from the front surface?

A) 0
B) 180°
C) λ/2
D) π/2
E) 55°

Question 8

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 9

The light reflected from a soap bubble (n = 1.40) appears red (λ = 640 nm) at its center. What is the minimum thickness (in nm)?

A) 124
B) 104
C) 114
D) 134
E) 234

Question 10

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 11

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 12

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 13

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°

Question 14

In a Newton's rings apparatus, find the phase difference (in radians) when an air wedge of 500 nm thickness is illuminated with red light (λ = 640 nm).

A) 13
B) 11
C) 9
D) 7
E) 3

Question 15

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 16

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 17

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 18

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 E_p = E_R 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 19

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 500-nm thick. Calculate the change of phase of the light that penetrates the front surface, reflects from the second surface, and emerges through the first surface as an angle between 0° and 360°?

A) 280°
B) 160°
C) 220°
D) 100°
E) 290°

Question 20

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.40). How thick is the bubble (in nm) if destructive interference occurs in the reflected light?

A) 102
B) 179
C) 54
D) 1
E) 89

Question 21

A film of index of refraction n₁ coats a surface with index of refraction n₂. When n₁ > n₂, the condition for destructive interference for reflected monochromatic light of wavelength λ in air is

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

Question 22

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 23

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 24

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. The locations of bright and dark fringes can be interchanged if a thin film is placed in front of one of the slits. The minimum thickness of this film must be

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

Question 25

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 26

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 27

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 28

A film of index of refraction n₁ coats a surface with index of refraction n₂. When n₁ > n₂, the condition for constructive interference for reflected monochromatic light of wavelength λ in air is

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

Question 29

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. Each bright fringe will shift to the location of the adjacent bright fringe if a thin film is placed in front of one of the slits. The minimum thickness of this film must be

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

Question 30

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 31

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 32

A film of index of refraction n₁ coats a surface with index of refraction n₂. When n₁ < n₂, the condition for destructive interference for reflected monochromatic light of wavelength λ in air is

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

Question 33

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.

Question 34

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 35

A film of index of refraction n₁ coats a surface with index of refraction n₂. When n₁ < n₂, the condition for constructive interference for reflected monochromatic light of wavelength λ in air is

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

Question 36

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 37

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 38

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 0.010 0 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 39

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 40

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 41

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 42

A soap bubble (n = 1.35) is floating in air. If the thickness of the bubble wall is 115 nm, what visible light wavelength is most strongly reflected?

Question 43

Nonreflective coatings for camera lenses reduce the loss of light at various surfaces of multi-lens systems, as well as preventing internal reflections that might mar the image. Find the minimum thickness of a layer of magnesium fluoride (n = 1.38) on flint glass (n = 1.66) that will cause destructive interference of reflected light of wavelength λ = 550 nm, a wavelength which is near the middle of the visual spectrum.

Question 44

A uniform film of oil (n = 1.31) is floating on water. When sunlight in air is incident normally on the film, an observer finds that the reflected light has a brightness maximum at λ = 450 nm and a brightness minimum at λ = 600 nm. What is the thickness of the oil film?

Question 45

In a double-slit experiment using light of wavelength 486 nm, the slit spacing is 0.600 mm and the screen is 2.00 m from the slits. Find the distance along the screen between adjacent bright fringes.

Question 46

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 47

Suppose two flat glass plates 30-cm long are in contact along one end and separated by a human hair at the other end. If the diameter of the hair is 50 μm, find the separation of the interference fringes when the plates are illuminated by green light, λ = 546 nm.

Question 48

When the adjustable mirror on the Michelson interferometer is moved 20 wavelengths, how many fringe pattern shifts would be counted?

A) 5
B) 10
C) 20
D) 40
E) 80