Deck 38: Diffraction Patterns and Polarization

Question 1

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°

Answer 1

3.67°

Question 2

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°

Answer 2

18.4°

Question 3

Sunlight reflected from a smooth ice surface is completely polarized.Determine the angle of incidence.(n_ice = 1.31. )

A)52.6°
B)25.6°
C)65.2°
D)56.2°
E)49.8°

Answer 3

52.6°

Question 4

Light reflected off a plate-glass window (n = 1.5)is found to be completely polarized at angle-of-incidence θ.Find θ.

A)56.3°
B)5.7°
C)21.2°
D)18.6°
E)33.7°

Question 5

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 6

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 7

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 8

Unpolarized light is passed through three successive Polaroid filters,each with its transmission axis at 45.0° to the preceding filter.What percentage of light gets through?

A)0%
B)12.5%
C)25.0%
D)50.0%
E)33.3%

Question 9

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 10

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 11

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 12

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 13

How far above the horizon is the moon when its image,reflected in a calm lake,is completely polarized? (n_water = 1.33. )

A)22.2°
B)7.7°
C)16.6°
D)36.9°
E)53.1°

Question 14

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/sec.

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

Question 15

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 16

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 17

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 18

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

Question 19

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 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

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 22

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 23

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 24

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 25

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 26

If the polarizing angle (the angle at which reflected light is completely plane polarized)of a flat piece of sapphire is 60.5°,what is its index of refraction?

A)1.97
B)1.77
C)1.59
D)2.36
E)1.82

Question 27

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 28

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 29

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)

Question 30

You could determine the index of refraction for visible light of a dark but reflective medium such as black glass by measuring the

A)angles of incidence and refraction.
B)angle of reflection for an arbitrary angle of incidence.
C)angle at which reflected light is completely polarized.
D)smallest angle at which X-ray diffraction occurs in the glass.
E)smallest angle at which diffraction occurs for visible light when a diffraction pattern is scratched onto the surface.

Question 31

Polarized light is to have its polarization plane rotated by 90°.In which of the following cases does the final beam have the greatest intensity?

A)3 polarizing filters,each rotate beam by 30°.
B)2 polarizing filters,both rotate beam by 45°.
C)1 polarizing filter,rotating beam by 90°.
D)None of the above,polarized light can't be rotated.

Question 32

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 33

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 34

The polarizing angle in air for diamond is 67.4°.Calculate the critical angle inside the diamond for total internal reflection.

A)32.6°
B)22.6°
C)24.6°
D)28.6°
E)48.8°

Question 35

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 36

If the polarizing angle for cubic zirconia (zirconium oxide)is 65.6°,what is the index of refraction of the material?

A)1.84
B)2.00
C)2.20
D)2.43
E)1.17

Question 37

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 38

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 39

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 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 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 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

The spacing between reflecting planes in a crystal is 2.82 × 10−¹⁰ m.A beam of X-rays is strongly reflected at an angle of 160° with the crystal face.What is the wavelength of the X-rays?

Question 43

A diffraction grating with 4000 lines/cm is illuminated by light from the sun.The solar spectrum is spread out on a white wall across the room.At what angle from the center line does blue light (400 nm)appear? At what angle from the center line does red light (650 nm)appear?

Question 44

Suppose a 5.0-meter diameter telescope were constructed on the dark side of the moon.The viewing there (except for brief periods of sunlight)would be excellent.As an example,what would be the separation between two objects that could just be resolved on the planet Mars in 500 nm light? [The distance to Mars at closest approach is 50 million miles.]

Question 45

Light strikes a flat water surface (n = 1.333)at the Brewster angle.Calculate the angle between the reflected and the refracted ray.

Question 46

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 47

Jane's flashy boy friend has just given her a ring with a huge "diamond".Jane,who has studied physics,measures the polarizing angle for the stone and finds that the polarizing angle is 62.97°.The stone is

A)fluoride,n = 1.560.
B)crown glass,n = 1.517.
C)spinel,n = 1.712.
D)zircon,n = 1.960.
E)diamond,n = 2.417.