Deck 35: Diffraction and Polarization

Question 1

In a single slit diffraction pattern the intensity of the maxima

A)are all the same.
B)increase with the sine of the angle from the central maximum.
C)decrease with the sine of the angle from the central maximum.
D)are proportional to the square of the sine of the angle from the central maximum.
E)depend upon the wavelength, the slit width, and the angle from the central maximum.

Answer 1

depend upon the wavelength, the slit width, and the angle from the central maximum.

Question 2

In a single-slit diffraction experiment, the first minimum in the diffraction pattern occurs at an angle given by sinθ = 2λ/W.

Answer 2

False

Question 3

Placing the Hubble Space Telescope in space gives better resolution because it is

A)above the atmosphere which distorts images.
B)in circular orbit where there is no spherical aberration.
C)in elliptical orbit where there is no spherical aberration.
D)larger than the largest ground-based telescopes.
E)free from gravity-produced optical flaws.

Answer 3

above the atmosphere which distorts images.

Question 4

If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged? Its resolving power

A)quadruples.
B)doubles.
C)halves.
D)is reduced to one-quarter its original value.
E)is reduced to one-half its original value.

Question 5

State the Rayleigh criterion.

Question 6

If the first maximum of one circular diffraction pattern passes through the center of a second diffraction pattern, the two sources responsible for the pattern will appear to be a single source.

Question 7

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the distance from the slit to the screen is doubled?

A)It will be cut to one-quarter its original size.
B)It will be cut in half.
C)It will double.
D)It will become four times as large.
E)It will become eight times as large.

Question 8

In a single-slit diffraction experiment, the central maximum is broadened if the wavelength of light is increased.

Question 9

If the lens diameter is doubled, what happens to the resolvable angle of images produced at fixed wavelength?

A)The angle decreases by a factor of two.
B)The angle increases by a factor of two.
C)The angle decreases by a factor of four.
D)The angle increases by a factor of four.
E)The angle stays the same.

Question 10

If in a single slit diffraction experiment the wavelength is increased, which of the following happens to the diffraction pattern?

A)The central maximum broadens.
B)The minima remain the same.
C)Eventually you get double slit interference.
D)The central maximum narrows.
E)The minima get closer together.

Question 11

The resolving power of a microscope refers to the ability to

A)distinguish objects of different colors.
B)form clear images of two points that are very close together.
C)form a very small image.
D)form a very large image.
E)form a very bright image.

Question 12

What principle is responsible for light spreading as it passes through a narrow slit?

A)refraction
B)reflection
C)polarization
D)diffraction
E)interference

Question 13

A lens is designed to work in the visible, near-infrared, and near-ultraviolet. The best resolution of this lens from a diffraction standpoint is

A)equal for all wavelengths.
B)in the near-ultraviolet.
C)in the visible.
D)in the near-infrared.
E)indeterminate.

Question 14

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the wavelength is doubled?

A)It will be cut to one-quarter its original size.
B)It will be cut in half.
C)It will double.
D)It will become four times as large.
E)It will become eight times as large.

Question 15

In a single-slit diffraction experiment, the width of the slit through which light passes is reduced. What happens to the central bright fringe?

A)It stays the same.
B)It becomes narrower.
C)It becomes wider.
D)We must know the wavelength of the light to answer.
E)We must know the distance from the slit to the screen to answer.

Question 16

Consider two diffraction gratings; one has 4000 lines per cm and the other one has 6000 lines per cm. Make a statement comparing the dispersion of the two gratings.

A)The 4000-line grating produces the greater dispersion.
B)The 6000-line grating produces the greater dispersion.
C)Both gratings produce the same dispersion, but the orders are sharper for the 4000-line grating.
D)Both gratings produce the same dispersion, but the orders are sharper for the 6000-line grating.

Question 17

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the slit width is doubled?

A)It will be cut to one-quarter its original size.
B)It will be cut in half.
C)It will double.
D)It will become four times as large.
E)It will become eight times as large.

Question 18

It is not possible to resolve detail of objects smaller than the wavelength of the radiation being used.

Question 19

Using the Rayleigh criterion, one concludes that using fixed wavelength light that it is not possible to resolve details less than about

A)0.5 wavelength.
B)0.1 wavelength.
C)one wavelength.
D)10 wavelengths.
E)122 wavelengths.

Question 20

An important reason for using a very large diameter objective in an astronomical telescope is

A)to increase the magnification.
B)to increase the resolution.
C)to form a virtual image, which is easier to look at.
D)to increase the width of the field of view.
E)to increase the depth of the field of view.

Question 21

A single slit, which is 0.050 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?

A)0.36°
B)0.47°
C)0.54°
D)0.63°
E)0.73°

Question 22

The polarization of sunlight is greatest at

A)sunrise.
B)sunset.
C)both sunrise and sunset.
D)midday.
E)remains constant throughout the day.

Question 23

If the 5th order minimum in the diffraction pattern is at 40°, at what angle is the 1st order minimum?

A)8.0°
B)3.4°
C)4.0°
D)7.4°
E)1.7°

Question 24

If the central maximum in a single slit diffraction pattern has intensity I_o, the intensity of the secondary maximum nearest it is

A)0.045 I_o.
B)0.50 I_o.
C)also I_o.
D)2 I_o.
E)0.25 I_o.

Question 25

Consider two diffraction gratings with the same slit separation, the only difference being that one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic light, make a statement concerning the separation between the orders.

A)The grating with 3 slits produces the greater separation between orders.
B)The grating with 4 slits produces the greater separation between orders.
C)Both gratings produce the same separation between orders, but the orders are better defined with the 3-slit grating..
D)Both gratings produce the same separation between orders, but the orders are better defined with the 4-slit grating.

Question 26

What principle is responsible for the fact that certain sunglasses can reduce glare from reflected surfaces?

A)refraction
B)reflection
C)polarization
D)diffraction
E)total internal reflection

Question 27

Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is produced on a screen that is 1.5 m from the slit. What is the width of the central maximum?

A)0.34 cm
B)0.46 m
C)0.68 cm
D)0.92 cm
E)1.2 cm

Question 28

If the 5th order minimum in the diffraction pattern is at 40°, what is the highest order minimum in the pattern?

A)6
B)11
C)8
D)7
E)9

Question 29

Light of wavelength 580 nm is incident on a slit of width 0.300 mm. An observing screen is placed 2.00 m from the slit. Find the position of the first order dark fringe from the center of the screen.

A)0.26 mm
B)1.9 mm
C)3.9 mm
D)4.3 mm
E)7.7 mm

Question 30

The discoverer of X-rays was

A)Bragg.
B)von Laue.
C)Fermi.
D)Roentgen.
E)Xavier.

Question 31

A slit of width 0.01 mm has light of wavelength 600 nm passing through it onto a screen 60 cm away. How wide (in cm) is the central maximum?

A)0.12 cm
B)7.2 cm
C)1.8 cm
D)3.6 cm
E)0.9 cm

Question 32

Sunlight reflected from the surface of a lake

A)is unpolarized.
B)tends to be polarized with its electric field vector parallel to the surface of the lake.
C)tends to be polarized with its electric field vector perpendicular to the surface of the lake.
D)has undergone refraction by the surface of the lake.
E)none of the given answers

Question 33

On a clear day, the sky appears to be more blue toward the zenith (overhead) than it does toward the horizon. This occurs because

A)the atmosphere is denser higher up than it is at the Earth's surface.
B)the temperature of the upper atmosphere is higher than it is at the Earth's surface.
C)the sunlight travels over a longer path at the horizon, resulting in more scattering.
D)none of the given answers

Question 34

Light of wavelength 580 nm is incident on a slit of width 0.300 mm. An observing screen is placed 2.00 m from the slit. Find the width of the central maximum.

A)0.26 mm
B)1.9 mm
C)3.9 mm
D)4.3 mm
E)7.7 mm

Question 35

For a beam of light, the direction of polarization is defined as

A)the beam's direction of travel.
B)the direction of the electric field's vibration.
C)the direction of the magnetic field's vibration.
D)the direction that is mutually perpendicular to the electric and magnetic field vectors.

Question 36

If light of wavelength 700 nm is sent through a slit of width of 5.0 μm, at what angle from the central maximum is the 4th order minimum?

A)90°
B)34°
C)39°
D)8°
E)68°

Question 37

When the transmission axes of two Polaroid films are perpendicular to each other, what is the percentage of the incident light which will pass the two films?

A)0%
B)25%
C)50%
D)75%
E)100%

Question 38

What is θ_min for a monochromatic beam of light of wavelength 600 nm and an aperture diameter of 6.00 mm?

A)100 × 10^-6 rad
B)202 × 10^-6 rad
C)122 × 10^-6 rad
D)244 × 10^-6 rad
E)236 × 10^-6 rad

Question 39

A slit of width 2.0 μm is used in a single slit experiment with light of wavelength 650 nm. If the intensity at the central maximum is I_o, what is the intensity 10° from the center?

A)0.53 I_o
B)0.03 I_o
C)0.43 I_o
D)0.50 I_o
E)0.35 I_o

Question 40

Light of wavelength 687 nm is incident on a single slit 0.75 mm wide. At what distance from the slit should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the screen?

A)0.39 m
B)0.47 m
C)0.93 m
D)1.1 m
E)1.9 m

Question 41

A 10-inch telescope is used to determine if what appears to be one star is actually two stars. Stars are so far away that they are essentially point sources. How close, in angle, can two stars be and still be resolved by this telescope? Use a wavelength of 550 nm.

A)4.2 × 10^-8 degree
B)2.64 × 10^-6 degree
C)3.0 × 10^-4 degree
D)1.5 × 10^-4 degree
E)6.6 × 10^-8 degree

Question 42

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, a wavelength of light of 600 nm and index of refraction for the eye equal to 1.34?

A)4.2 × 10^-4 rad
B)2.1 × 10^-4 rad
C)1.4 × 10^-4 rad
D)1.1 × 10^-4 rad
E)2.6 × 10^-4 rad

Question 43

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, at what angle does the first order maximum occur?

A)56°
B)44°
C)22°
D)11°
E)28°

Question 44

A 200-m radio telescope is used to investigate sources emitting a 21-cm wavelength. The minimum angular separation resolvable for this system is

A)0.073°.
B)0.03°.
C)0.0013°.
D)0.154°.
E)0.0026°.

Question 45

A diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is 47.2°. What is the wavelength of the light?

A)138 nm
B)183 nm
C)367 nm
D)452 nm
E)637 nm

Question 46

The angular resolution of the eye is about 5 × 10^-4 rad. The Moon is about 400,000 km from the earth and has a diameter of about 3500 km. What is the smallest feature on the Moon that can be resolved with the unaided eye?

A)400 km
B)1000 km
C)100 km
D)1.8 km
E)200 km

Question 47

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is about 5 × 10^-4 rad?

A)1.3 km
B)5.0 km
C)4.8 km
D)0.65 km
E)2.6 km

Question 48

In a diffraction experiment, light of 600 nm wavelength produces a first-order maximum 0.350 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum 0.870 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source?

A)479 nm
B)497 nm
C)567 nm
D)749 nm
E)794 nm

Question 49

The limiting angle of resolution for the eye is 1.4 × 10^-4 rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?

A)2.8 × 10^-3 m
B)5.6 × 10^-3 m
C)1.4 × 10^-3 m
D)8.4 × 10^-3 m
E)4.7 × 10^-3 m

Question 50

Monochromatic light is incident on a grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light?

A)202 nm
B)403 nm
C)452 nm
D)605 nm
E)806 nm

Question 51

A He-Ne laser (632.8 nm) is used to calibrate a grating. If the first-order maximum occurs at 20.5°, what is the grating constant (the distance between the slits)?

A)0.905 μm
B)1.81 μm
C)2.20 μm
D)3.62 μm
E)4.52 μm

Question 52

White light is spread out into spectral hues by a grating. If the grating has 2000 lines per centimeter, at what angle will red light (640 nm) appear in the first order?

A)3.57°
B)7.35°
C)11.2°
D)13.4°
E)14.7°

Question 53

A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A)1.11 × 10^-7 rad
B)3.11 × 10^-7 rad
C)2.70 × 10^-7 rad
D)1.35 × 10^-7 rad
E)4.05 × 10^-7 rad

Question 54

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

A)8
B)2
C)6
D)5
E)5.3

Question 55

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, what is the grating constant (distance between the slits)?

A)0.93 μm
B)1.4 μm
C)2.8 μm
D)5.6 μm
E)8.5 μm

Question 56

What resolving power is needed to resolve spectral lines at 651.22 nm and 651.81 nm?

A)1100
B)1000
C)1200
D)1400
E)1300

Question 57

A telescope that uses a mirror 249 cm in diameter is just able to resolve a double-star system that is 1.5 light-years away. Assume the light from the stars has a wavelength of 691 nm. How far apart are the two stars? One light year = 9.46 × 10¹⁵ m. (Use the approximation for θ_min: θ_min ≈ .)

A)9.8 × 10⁷ m
B)8.5 × 10⁸ m
C)8.5 × 10⁹ m
D)9.8 × 10⁸ m
E)4.8 × 10⁹ m

Question 58

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, how many total number of maxima can be seen?

A)5
B)7
C)10
D)11
E)13

Question 59

A diffraction grating has 6000 lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength 550 nm?

A)12.3°
B)20.5°
C)30.5°
D)40.5°
E)50.5°

Question 60

When light illuminates a grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?

A)336 nm
B)363 nm
C)452 nm
D)633 nm
E)752 nm

Question 61

How far above the horizon is the Moon when its image reflected in calm water is completely polarized?

A)36.9°
B)43.2°
C)46.8°
D)53.1°
E)57.5°

Question 62

A beam of unpolarized light in air strikes a flat piece of glass at an angle of 57.3°. If the reflected beam is completely polarized, what is the index of refraction of the glass?

A)1.50
B)1.52
C)1.54
D)1.56
E)1.58

Question 63

Unpolarized light is passed through a polarizer-analyzer combination. The transmission axes of the polarizer and the analyzer are at 30.0° to each other. What percentage of the unpolarized light gets through the combination?

A)37.5%
B)50.0%
C)63.7%
D)75.0%
E)100%

Question 64

A beam of light passes through a polarizer and then an analyzer. In this process, the intensity of the light transmitted is reduced to 10% of the intensity incident on the analyzer. What is the angle between the axes of the polarizer and the analyzer?

A)18°
B)22°
C)68°
D)72°

Question 65

If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference, at what angle will the second order line appear?

A)40°
B)20°
C)43°
D)4°
E)11°

Question 66

An ideal polarizer is placed in a beam of unpolarized light and the intensity of the transmitted light is 1. A second ideal polarizer is placed in the beam with its preferred direction rotated 40° to that of the first polarizer. What is the intensity of the beam after it has passed through both polarizers?

A)0.77
B)0.64
C)0.59
D)0.41
E)0.30

Question 67

If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference, what is the plane spacing?

A)2.8 × 10^-10 m
B)0.7 × 10^-10 m
C)3.2 × 10^-10 m
D)1.6 × 10^-10 m
E)1.4 × 10^-10 m

Question 68

A polarizer (with its preferred direction rotated 30° to the vertical) is placed in a beam of unpolarized light of intensity 1. After passing through the polarizer, the beam's intensity is

A)0.25.
B)0.50.
C)0.63.
D)0.87.
E)0.75.