Deck 28: Sources of Magnetic Field

Question 1

Double-slit interference: In a double slit experiment, if the separation between the two slits is 0.050 mm and the distance from the slits to a screen is 2.5 m, find the spacing between the first-order and second-order bright fringes when coherent light of wavelength 600 nm illuminates the slits.

A) 1.5 cm
B) 3.0 cm
C) 4.5 cm
D) 6.0 cm
E) 9.0 cm

Answer 1

3.0 cm

Question 2

Double-slit interference: Light of wavelength 575 nm passes through a double-slit and the third order bright fringe is seen at an angle of 6.5° away from the central fringe. What is the separation between the double slits?

A) 5.0 µm
B) 10 µm
C) 15 µm
D) 20 µm
E) 25 µm

Answer 2

15 µm

Question 3

Double-slit interference: In the two-slit experiment, monochromatic light of frequency 5.00 × 10¹⁴ Hz passes through a pair of slits separated by 2.20 × 10^-5 m. (c = 3.00 × 10⁸ m/s)
(a) At what angle away from the central bright spot does the third bright fringe past the central bright spot occur?
(b) At what angle does the second dark fringe occur?

Answer 3

(a) 4.69°
(b) 2.34°

Question 4

Double-slit interference: In a two-slit experiment, the slit separation is 3.00 × m. The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits. If the seventh bright fringe on the detector is 10.0 cm away from the central fringe, what is the wavelength of the light passing through the slits?

A) 100 nm
B) 204 nm
C) 214 nm
D) 224 nm
E) 234 nm

Question 5

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

A) It stays the same.
B) It becomes narrower.
C) It becomes wider.
D) Its behavior depends on the wavelength of the light.

Question 6

Double-slit interference: In a double slit experiment, the slit separation is constructed to be exactly 4 times the wavelength of the light passing through the slits. At what angles from the center of the pattern will the third bright fringes on both sides of the central fringe occur?

A) ±48.6°
B) ±75.0°
C) ±67.5°
D) ±36.9°
E) ±43.0°

Question 7

Single-slit diffraction: A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the screen is 1.00 cm wide, as measured between the dark fringes that border it on either side. Which of the following actions would decrease the width of the central bright fringe? (There may be more than one correct choice.)

A) increase the wavelength of the light
B) decrease the wavelength of the light
C) increase the width of the slit
D) decrease the width of the slit
E) put the apparatus all under water

Question 8

Double-slit interference: A double slit illuminated with light of wavelength 588 nm forms a diffraction pattern on a screen 11.0 cm away. The slit separation is 2464 nm. What is the distance between the third and fourth bright fringes away from the central fringe?

A) 23.9 cm
B) 5.96 cm
C) 5.59 cm
D) 2.63 cm

Question 9

Double-slit interference: Light from a monochromatic source shines through a double slit onto a screen 5.00 m away. The slits are 0.180 mm apart. The dark bands on the screen are measured to be 1.70 cm apart. What is the wavelength of the incident light?

A) 457 nm
B) 306 nm
C) 392 nm
D) 612 nm
E) 784 nm

Question 10

Resolving power: 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) the same for all wavelengths.
B) in the near-ultraviolet.
C) in the visible.
D) in the near-infrared.
E) indeterminate.

Question 11

Single-slit diffraction: 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 12

Double-slit interference: A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. Light waves arrive at the two slits in phase, and a fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 complete bright fringes per centimeter on the screen near the center of the pattern, what is the wavelength of the monochromatic light?

A) 550 nm
B) 600 nm
C) 650 nm
D) 700 nm
E) 750 nm

Question 13

Double-slit interference: Light from a 600 nm source goes through two slits 0.080 mm apart. What is the angular separation of the two first order maxima occurring on a screen 2.0 m from the slits?

A) 0.15°
B) 0.86°
C) 0.015°
D) 0.0075°
E) 1.75°

Question 14

Double-slit interference: At most, how many bright fringes can be formed on each side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a double slit whose spacing is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 15

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

A) The resolving power quadruples.
B) The resolving power doubles.
C) The resolving power is reduced to 1/2 of its original value.
D) The resolving power is reduced to 1/4 of its original value.
E) The resolving power does not change unless the focal length changes.

Question 16

Double-slit interference: Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A woman is standing opposite the midpoint between the speakers and is initially 35.0 m from the midpoint. As she slowly walks parallel to the line connecting the speakers, at what angle θ (relative to the centerline coming outward from the midpoint between the speakers) will she first hear no sound?

A) 0.063°
B) 3.6°
C) 7.2°
D) 1.8°
E) 11°

Question 17

Double-slit interference: In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits simultaneously. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?

A) 1.5 mm
B) 3.0 mm
C) 4.5 mm
D) 6.0 mm
E) 9.0 mm

Question 18

Double-slit interference: Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s)

A) 43°
B) 22°
C) 68°
D) 47°
E) 30°

Question 19

Double-slit interference: In a double-slit experiment, if the slit separation is increased, which of the following happens to the interference pattern shown on the screen?

A) The minima get closer together.
B) The maxima stay at the same position.
C) The minima and maxima stay at the same position.
D) The minima stay at the same position.
E) The maxima get further apart.

Question 20

Double-slit interference: Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The bright fringe of the unknown wavelength overlaps the bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?

A) 456 nm
B) 326 nm
C) 380 nm
D) 713 nm

Question 21

Thin films: Light of wavelength 425.0 nm in air falls at normal incidence on an oil film that is 850.0 nm thick. The oil is floating on a water layer 15 cm thick. The refractive index of water is 1.33, and that of the oil is 1.40. You want to add oil so that light reflected off of the top of the oil film will be canceled. What is the minimum distance that you should INCREASE the oil film?

A) 60.7 nm
B) 75.9 nm
C) 106 nm
D) 121 nm
E) 152 nm

Question 22

Thin films: Light of frequency 6.00 × 10¹⁴ Hz illuminates a soap film (n = 1.33) having air on both sides of it. When viewing the film by reflected light, what is the minimum thickness of the film that will give an interference maximum when the light is incident normally on it? (c = 3.00 × 10⁸ m/s)

A) 24.0 nm
B) 94.0 nm
C) 188 nm
D) 279 nm
E) 376 nm

Question 23

Double-slit interference: Coherent monochromatic light of wavelength 632.8 nm passes through a pair of thin parallel slits. The figure shows the central portion of the pattern of bright fringes viewed on a screen 1.40 m beyond the slits. What is the distance between the two slits?

A) 0.0703 mm
B) 0.141 mm
C) 0.281 mm
D) 0.562 mm
E) 0.633 mm

Question 24

Double-slit interference: Light of wavelength 519 nm passes through two slits. In the interference pattern on a screen 4.6 m away, adjacent bright fringes are separated by 5.2 mm in the general vicinity of the center of the pattern. What is the separation of the two slits?

Question 25

Thin films: White light is incident normally on a thin soap film having an index of refraction of 1.34. It reflects with an interference maximum at 684 nm and an interference minimum at 570 nm with no minima between those two values. The film has air on both sides of it. What is the thickness of the soap film?

A) 766 nm
B) 627 nm
C) 638 nm
D) 894 nm
E) 510 nm

Question 26

Thin films: Two optically flat glass plates, 16.0 cm long, are in contact at one end and separated by 0.0200 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The index of refraction of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. If the dark fringes are spaced 2.00 mm apart, what is the wavelength of the monochromatic light?

A) 425 nm
B) 475 nm
C) 525 nm
D) 675 nm
E) 725 nm

Question 27

Intensity of double-slit pattern: Light of wavelength 525 nm passes through two slits separated by 0.500 mm and produces an interference pattern on a screen 7.80 m away. The intensity at the central maximum is I₀. What is the distance on the screen from the center of this central maximum to the point where the intensity due to double-slit interference has fallen to 1/2 I₀?

Question 28

Single-slit diffraction: A single slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum, when monochromatic light of 630-nm wavelength is used. The same slit, illuminated by a new monochromatic light source, produces a diffraction pattern with the second minimum at a 60.0° angle from the central maximum. What is the wavelength of this new light?

A) 425 nm
B) 450 nm
C) 475 nm
D) 500 nm
E) 525 nm

Question 29

Thin films: A soap bubble, when illuminated with light of frequency 5.11 × 10¹⁴ Hz, appears to be especially reflective. If it is surrounded by air and if its index of refraction is 1.35, what is the thinnest thickness the soap film can be? (c = 3.00 × 10⁸ m/s)

Question 30

Single-slit diffraction: A single slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum, using monochromatic light of 490-nm wavelength. What is the width of the slit?

A) 762 nm
B) 731 nm
C) 700 nm
D) 668 nm
E) 637 nm

Question 31

Intensity of double-slit pattern: In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m². What is the intensity halfway between the center of this fringe and the first dark band, assuming that the small-angle approximation is valid?

A) 6.2 µW/m²
B) 3.1 µW/m²
C) 4.7 µW/m²
D) 1.6 µW/m²
E) 0.12 µW/m²

Question 32

Thin films: A coating is being applied to reduce the reflectivity of a pane of glass to light with a frequency of 5.75 × 10¹⁴ Hz that is incident normally on the pane. If the material has an index of refraction of 1.375 and the glass has an index of refraction of 1.537, what is the minimum thickness the coating should have? (c = 3.00 × 10⁸ m/s)

A) 60.0 nm
B) 94.9 nm
C) 145 nm
D) 65.2 nm
E) 80.1 nm

Question 33

Thin films: Two extremely flat glass plates, 10.0 cm wide, touch at one end but are separated by a thin wire at the other end, forming a wedge. Light with a wavelength of 450 nm shines almost perpendicularly on the glass and forms fringes which are 1.80 mm apart. What is the diameter of the wire?

A) 25.0 µm
B) 17.5 µm
C) 20.0 µm
D) 12.5 µm
E) 10.0 µm

Question 34

Thin films: A piece of glass has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and glass are 1.40 and 1.50, respectively, what is the minimum nonzero thickness of the film to see a bright reflection?

A) 500 nm
B) 400 nm
C) 300 nm
D) 200 nm
E) 100 nm

Question 35

Thin films: A 360-nm thick oil film floats on the surface of the water. The indices of refraction of the oil and the water are 1.5 and 1.33, respectively. The surface of the oil is illuminated from above at normal incidence with white light. What TWO wavelengths of light in the 400-nm to 800-nm wavelength band are most strongly reflected?

A) 410 nm and 700 nm
B) 430 nm and 720 nm
C) 450 nm and 740 nm
D) 470 nm and 760 nm
E) 490 nm and 780 nm

Question 36

Double-slit interference: Monochromatic laser light of frequency 5.20 × 10¹⁴ Hz is shown on a pair of thin parallel slits, and the pattern is viewed on a screen 1.20 m away. The fifth bright fringes (not counting the central fringe) occur at ±2.12 cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent liquid. When the experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central bright fringe. (c = 3.00 × 10⁸ m/s)
(a) How far apart are the slits?
(b) What is the index of refraction of the liquid?

Question 37

Intensity of double-slit pattern: Light passes through a pair of very thin parallel slits. The resulting interference pattern is viewed far from the slits at various angles θ relative to the centerline coming outward from the midpoint between the slits. The central bright fringe is at θ = 0°. If the central bright fringe has intensity I₀, what is the intensity of the next bright fringe on either side of it?

A) I₀
B) I₀/
C) I₀/2
D) I₀ cos 15°
E) I₀ cos² 15°

Question 38

Thin films: Light is incident normally from air onto a liquid film that is on a glass plate. The liquid film is 164 nm thick, and the liquid has index of refraction 1.60. The glass has index of refraction n = 1.50. Calculate the longest visible wavelength (as measured in air) of the light for which there will be totally destructive interference between the rays reflected from the top and bottom surfaces of the film. (Assume that the visible spectrum lies between 400 and 700 nm.)

Question 39

Thin films: A thin layer of oil (n = 1.25) is on top of a puddle of water (n = 1.33). If normally incident 500-nm light is strongly reflected, what is the minimum nonzero thickness of the oil layer?

A) 200 nm
B) 250 nm
C) 100 nm
D) 400 nm
E) 150 nm

Question 40

Thin films: A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and water are 1.40 and 1.33, respectively, what is the minimum thickness of the film to see a bright reflection?

A) 100 nm
B) 200 nm
C) 300 nm
D) 400 nm
E) 500 nm

Question 41

Single-slit diffraction: A laser beam passes through a thin slit. When the pattern is viewed on a screen 1.25 m past the slit, you observe that the fifth-order dark fringes occur at ±2.41 cm from the central bright fringe. The entire experiment is now performed within a liquid, and you observe that each of the fifth-order dark fringes is 0.790 cm closer to the central fringe than it was in air. What is the index of refraction of this liquid?

A) 1.33
B) 1.40
C) 1.49
D) 1.62
E) 3.05

Question 42

Intensity of single-slit pattern: 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 I₀, what is the intensity 10° from the center?

A) 0.53I₀
B) 0.030I₀
C) 0.43I₀
D) 0.50I₀
E) 0.35I₀

Question 43

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

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

Question 44

Intensity of single-slit pattern: A single slit that is 2100 nm wide forms a diffraction pattern when illuminated by monochromatic light of 680-nm wavelength. At an angle of 10° from the central maximum, what is the ratio of the intensity to the intensity of the central maximum?

A) I/I₀ = 0.35
B) I/I₀ = 0.39
C) I/I₀ = 0.43
D) I/I₀ = 0.47
E) I/I₀ = 0.51

Question 45

Single-slit diffraction: If the fifth order minimum in the diffraction pattern of a thin slit is at 40° from the central maximum, what is the highest order minimum in the pattern?

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

Question 46

Single-slit diffraction: 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 47

Single-slit diffraction: If the fifth order minimum in the diffraction pattern due to a thin slit is at 40° from the central maximum, at what angle does the first order minimum occur?

A) 8.0°
B) 3.4°
C) 4.0°
D) 7.4°
E) 1.7°

Question 48

Single-slit diffraction: A single slit illuminated with a 500 nm light gives a diffraction pattern on a far screen. The 5^th minimum occurs at 7.00° away from the central maximum. At what angle does the 18^th minimum occur?

A) 26.0°
B) 1.94°
C) 5.05°
D) 0.44°

Question 49

Intensity of single-slit pattern: A thin beam of light of wavelength 625 nm goes through a thin slit and falls on a screen 3.00 m past the slit. You observe that the first completely dark fringes occur on the screen at distances of ±8.24 mm from the central bright fringe, and that the central bright fringe has an intensity of 2.00 W/m2 at its center.
(a) How wide is the slit?
(b) What is the intensity of light at a point on the screen that is one-quarter of the way from the central bright fringe to the first dark fringe?

Question 50

Intensity of single-slit pattern: If the central maximum in a single slit diffraction pattern has intensity I₀, the intensity of the secondary maximum that is nearest to it is closest to

A) 0.045I₀.
B) I₀/4.
C) I₀/2.
D) I₀.
E) 2I₀.

Question 51

Single-slit diffraction: A slit of width 0.010 mm has light of frequency 5.0 × 10¹⁴ Hz passing through it onto a screen 60 cm away. How wide is the central maximum? (c = 3.00 × 10⁸ m/s)

A) 0.12 cm
B) 7.2 cm
C) 1.8 cm
D) 3.6 cm
E) 0.90 cm

Question 52

Single-slit diffraction: In the figure, a slit 0.30 mm wide is illuminated by light of wavelength 426 nm. A diffraction pattern is seen on a screen 2.8 m from the slit. What is the linear distance on the screen between the first diffraction minima on either side of the central diffraction maximum?

Question 53

Single-slit diffraction: 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 diffraction pattern?

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

Question 54

Single-slit diffraction: A single slit forms a diffraction pattern with monochromatic light. The 4th minimum of the pattern occurs at an angle of 35° from the central maximum. How many bright bands are on each side of the central maximum?

A) 5
B) 4
C) 6
D) 7
E) 8

Question 55

Diffraction grating: 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 56

Diffraction grating: When monochromatic 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 57

Diffraction grating: A diffraction grating has 300 lines per mm. If light of frequency 4.76 × 10¹⁴ Hz is sent through this grating, at what angle does the first order maximum occur? (c = 3.00 × 10⁸ m/s)

A) 56°
B) 44°
C) 22°
D) 11°
E) 28°

Question 58

Diffraction grating: In a diffraction grating 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 59

Diffraction grating: 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 60

Diffraction grating: A He-Ne laser, which produces light of wavelength 632.8 nm, is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5° from the central spot, what is the distance between the slits of the grating?

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

Question 61

X-ray diffraction: Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of X-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes. What is the wavelength of the X-rays?

A) 0.14 nm
B) 0.17 nm
C) 0.21 nm
D) 0.24 nm
E) 0.27 nm

Question 62

Diffraction grating: What is the angular separation of the two second-order spectral lines having wavelengths 417 nm and 388 nm using a diffraction grating having 456 lines/mm?

A) 1.63°
B) 1.52°
C) 0.815°
D) 3.26°

Question 63

X-ray diffraction: 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) 4.0°
E) 11°

Question 64

Diffraction grating: An 18-mm wide diffraction grating has rulings of 880 lines per mm. Monochromatic light of 590 nm wavelength is incident normally on the grating. What is the largest angle, measured from the central bright spot, at which an intensity maximum is formed?

A) 31°
B) 29°
C) 27°
D) 25°
E) 23°

Question 65

Diffraction grating: A diffraction grating has rulings of 890 lines/mm. When white light is incident normally on the grating, what is the longest wavelength that forms an intensity maximum in the fifth order?

A) 225 nm
B) 200 nm
C) 250 nm
D) 275 nm
E) 300 nm

Question 66

Circular aperture: Light of wavelength 500 nm illuminates a round 0.50-mm diameter hole. A screen is placed 6.3 m behind the slit. What is the diameter of the central bright area on the screen?

A) 15 mm
B) 270 μm
C) 7.7 mm
D) 3800 μm

Question 67

Resolving power: 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 5.0 × 10^-4 rad and the person has excellent vision?

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

Question 68

Resolving power: What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, the wavelength of the light is 600 nm, and index of refraction of the liquid in the eye is 1.34?

A) 0.42 mrad
B) 0.21 mrad
C) 0.14 mrad
D) 0.11 mrad
E) 0.26 mrad

Question 69

Diffraction grating: A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the microwave wavelength is 6.0 cm, what is the largest angle away from the central maximum at which an intensity maximum occurs.

A) 64°
B) 69°
C) 74°
D) 79°
E) 84°

Question 70

Diffraction grating: A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. What is the smallest microwave frequency for which only the central maximum occurs? (c = 3.00 × 10⁸ m/s)

A) 0.50 GHz
B) 0.70 GHz
C) 1.0 GHz
D) 1.5 GHz
E) 2.0 GHz

Question 71

Diffraction grating: A diffraction grating has 450 lines per mm. What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?

A) m = 2
B) m = 3
C) m = 4
D) m = 5
E) m = 6

Question 72

X-ray diffraction: 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) 0.28 nm
B) 0.070 nm
C) 0.32 nm
D) 0.16 nm
E) 0.14 nm

Question 73

Resolving power: A certain astronomical telescope has a diameter of 5.60 m. Considering only the limitation due to diffraction, what is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A) 0.111 µrad
B) 0.311 µrad
C) 0.270 µrad
D) 0.135 µrad
E) 0.405 µrad

Question 74

Diffraction grating: A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot. If the experiment were performed with all of the apparatus under water (which has an index of refraction of 1.33), what would be the TOTAL number of bright spots that would show up on the screen?

A) 6
B) 7
C) 12
D) 13
E) 14

Question 75

Circular aperture: Light of wavelength 633 nm from a He-Ne laser passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The diameter of the central bright area is 5.4 cm. What is the diameter of the aperture?

A) 110 μm
B) 2.0 μm
C) 6600 μm
D) 960 μm

Question 76

Resolving power: A radio telescope 200 m in diameter is used to investigate sources emitting a 21-cm wavelength wave. What is the minimum angular separation of the sources that can be resolved by this system?

A) 0.073°
B) 0.030°
C) 0.0013°
D) 0.154°
E) 0.0026°

Question 77

Diffraction grating: A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot. What is the TOTAL number of bright fringes that will show up on the screen?

A) 4
B) 5
C) 8
D) 9
E) 10

Question 78

Diffraction grating: A diffraction grating is to be used to find the wavelength of the light in the emission spectrum of a gas. The grating spacing is not known, but a light having a known wavelength of 632.8 nm is deflected by 43.2° away from the central maximum in the second order by this grating. Light of the wavelength to be measured is deflected by 48.2° away from the central maximum in the second order. What is the wavelength of this light?

Question 79

X-ray diffraction: A researcher is investigating a cubic crystal with X-rays. He is looking at Bragg reflection from the planes parallel to the cube faces. He finds that when using X-rays of 0.165 nm a strong first maximum occurs when the beam makes an angle of 23.5° with the planes. What is the spacing of adjacent atoms in the crystal?

Question 80

Resolving power: A 10-inch telescope (25.4 cm in diameter) 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 the two stars be and still be resolved by this telescope if it is focusing light of wavelength of 550 nm? (Consider only the limitation due to diffraction.)

A) 4.2 × 10^-8 degree
B) 2.6 × 10^-6 degree
C) 3.0 × 10^-4 degree
D) 1.5 × 10^-4 degree
E) 6.6 × 10^-8 degree