Deck 36: Applications of the Wave Model

Question 1

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?

Answer 1

343.5 nm

Question 2

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) .

Answer 2

.

Question 3

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

Answer 3

114

Question 4

At what distance could one theoretically distinguish two automobile headlights separated by 1.5 meters? Assume a pupil diameter of 0.50 cm and yellow headlights seen at the wavelength 5.0 × 10−7 m. Assume eye fluid has an average n = 1.33.

A)6.0 km
B)12 km
C)9.0 km
D)3.0 km
E)16 km

Question 5

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 6

A ruby laser beam (λ = 694.3 nm) is sent outwards from a 2.7-m diameter telescope to the Moon, 384,000 km away. What is the radius of the big red spot on the Moon?

A)500 m
B)250 m
C)120 m
D)1.0 km
E)2.7 km

Question 7

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 8

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 width of this film must be

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

Question 9

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 10

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 11

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

Question 12

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 13

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 14

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 15

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 width of this film must be

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

Question 16

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 17

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 18

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 19

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 20

The large space telescope that has been placed into an Earth orbit has an aperture diameter of 2.40 meters. What angular resolution will this telescope achieve for visible light of wavelength λ = 4.80 × 10−7 m?

A)2.44 × 10−7 rads
B)2.44 × 10−4 rads
C)2.44 × 10−3 rads
D)1.22 × 10−6 rads
E)2.00 × 10−6 rads

Question 21

What, approximately, are the dimensions of the smallest object on Earth that the astronauts can resolve by eye at 200 km height from the space shuttle? Assume λ = 500 nm light and a pupil diameter D = 0.50 cm. Assume eye fluid has an average n = 1.33.

A)150 m
B)100 m
C)250 m
D)25 m
E)18 m

Question 22

Monochromatic light from a He-Ne laser (λ = 632.8 nm) is incident on a diffraction grating containing 5000 lines/cm. Determine the angle of the first-order maximum.

A)18.4°
B)39.2°
C)14.6°
D)27.7°
E)13.9°

Question 23

White light is spread out into spectral hues by a diffraction grating. If the grating has 1000 lines per cm, at what angle will red light (λ = 640 nm) appear in first order?

A)14.7°
B)7.35°
C)17.7°
D)3.67°
E)1.84°

Question 24

If the interplanar spacing of NaCl is 2.814 × 10−10 m, what is the predicted angle at which X-rays of wavelength 0.140 nm will be diffracted in a first-order maximum?

A)31.3°
B)7.20°
C)20.5°
D)14.4°
E)29.8°

Question 25

In an X-ray diffraction experiment using X-rays of λ = 0.500 × 10−10 m, a first-order maximum occurred at 5.00°. Find the crystal plane spacing.

A)2.87 × 10−10 m
B)1.36 × 10−10 m
C)6.24 × 10−9 m
D)1.93 × 10−9 m
E)5.74 × 10−9 m

Question 26

Potassium Iodide (chemical formula: KI) has a face-centered cubic structure (just like sodium chloride). If the distance between crystal planes is d = 0.353 nm and X-rays of wavelength λ = 0.0934 nm are used, what is the smallest angle θ at which a diffraction maximum may be obtained?

A)9.92°
B)7.60°
C)13.3°
D)15.5°
E)6.52°

Question 27

The hydrogen spectrum has a red line at 656 nm, and a blue line at 434 nm. What is the first order angular separation between the two spectral lines obtained with a diffraction grating with 5000 rulings/cm?

A)7.7°
B)16.6°
C)6.6°
D)3.2°
E)19.2°

Question 28

A radar installation operates at 9000 MHz with an antenna (dish) that is 15 meters across. Determine the maximum distance (in kilometers) for which this system can distinguish two aircraft 100 meters apart.

A)7.4 km
B)370 km
C)3700 m
D)37 km
E)740 km

Question 29

A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 × 10−5 radians. If λ = 5 × 10−7 m, what is the smallest-aperture (diameter) telescope that may be used to resolve the two stars?

A)10 cm
B)5 cm
C)50 cm
D)1 m
E)4 cm

Question 30

A helium-neon laser (λ = 632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5°, what is the line spacing, d?

A)1.81 × 10−6 m
B)1.00 × 10−5 m
C)1.00 × 10−4 m
D)1.31 × 10−6 m
E)6.76 × 10−7 m

Question 31

A beam of X-rays of different frequencies is reflected at 10 degrees off a crystal of interatomic spacing 0.2 nm. Which X-ray wavelength is preferentially reflected?

A)0.0943 nm
B)0.139 nm
C)0.0695 nm
D)1.02 × 10−10 m
E)3.47 × 10−11 m