Deck 34: Interference

Question 1

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°

Answer 1

±48.6°

Question 2

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

Answer 2

0.281 mm

Question 3

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

Answer 3

4.5 mm

Question 4

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 5

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 1.97 × 10^-6 m?

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

Question 6

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 7

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 8

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?

Question 9

In a two-slit experiment, the slit separation is 3.00 × 10^-5 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 10

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 11

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 12

Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The m = 5 bright fringe of the unknown wavelength overlaps the m = 4 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 13

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

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

Question 15

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 16

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

Question 17

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 18

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 19

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 20

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 21

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 22

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 23

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 24

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 25

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

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 27

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 28

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 29

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 30

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 31

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 32

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 33

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