Deck 13: Interference and Diffraction

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Question
Two waves, one with amplitude A and the second with amplitude 2A, are out of phase by 180 °\degree . The resultant intensity is

A) zero
B) A
C) A2
D) 2A2
E) (3A)2
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Question
<strong>  In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is</strong> A) 1 only B) 2 only C) 3 only D) 1 and 2 E) 2 and 3 <div style=padding-top: 35px> In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is

A) 1 only
B) 2 only
C) 3 only
D) 1 and 2
E) 2 and 3
Question
 <strong>  The phase difference for the two waves shown in the figure is</strong> A) 2  \pi  B)   \pi  C) 3  \pi /2 D)   \pi /2 E) It is not possible to answer this question without additional information. <div style=padding-top: 35px>  The phase difference for the two waves shown in the figure is

A) 2 π\pi
B) π\pi
C) 3 π\pi /2
D) π\pi /2
E) It is not possible to answer this question without additional information.
Question
Two waves, one with amplitude A and the second with amplitude 2A, are in phase. The resultant intensity is

A) zero
B) A
C) 3A
D) 3A2
E) (3A)2
Question
Visible light from an ordinary source such as a sodium lamp can be used to produce interference effects that demonstrate the wave nature of light, provided that

A) the light beam from the single source is split into two (or more) beams that have a constant phase relationship to one another.
B) the light is polarized.
C) the light is not polarized.
D) Interference effects cannot be demonstrated with ordinary light sources.
E) None of these conditions are satisfied.
Question
For us to see interference phenomena in a thin film,

A) the incoming light must be monochromatic.
B) the index of refraction of the thin film must be greater than the index of refraction of the material below it.
C) the index of refraction of the thin film must be less than the index of refraction of the material below it.
D) the incoming light must be multicolored.
E) none of these conditions need exist
Question
The minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is

A) 600 nm
B) 500 nm
C) 300 nm
D) 200 nm
E) 100 nm
Question
 <strong>  The path difference for the two waves shown in the figure could be</strong> A) ¾ \lambda  B) ½ \lambda  C) ¼ \lambda  D) \lambda  E) It is not possible to answer this question without additional information. <div style=padding-top: 35px>  The path difference for the two waves shown in the figure could be

A) ¾ λ\lambda
B) ½ λ\lambda
C) ¼ λ\lambda
D) λ\lambda
E) It is not possible to answer this question without additional information.
Question
Two side-by-side coherent light sources radiate at 633 nm. At a point in space where the path difference to these two sources is 30 nm, the phase difference could be

A) 0.238 radians
B) 0.298 radians
C) 0.324 radians
D) 0.356 radians
E) 0.429 radians
Question
 <strong>  Why are fringes not observed if the angle of the wedge of air in the diagram is too large?</strong> A) For a large angle, the small-angle approximation (sin  \theta   \approx   \theta ) is not valid. B) the light passing through the wedge of air loses its coherence C) the fringes overlap D) the fringes are too close together to be seen individually E) None of these is correct. <div style=padding-top: 35px>  Why are fringes not observed if the angle of the wedge of air in the diagram is too large?

A) For a large angle, the small-angle approximation (sin θ\theta \approx θ\theta ) is not valid.
B) the light passing through the wedge of air loses its coherence
C) the fringes overlap
D) the fringes are too close together to be seen individually
E) None of these is correct.
Question
 <strong>  Two coherent sources of monochromatic light are located at S<sub>1</sub> and S<sub>2</sub> as shown. If the sources are in phase, the intensity at point P is a maximum when</strong> A) d = \lambda  B) r<sub>2</sub> + r<sub>1</sub> =  \lambda  C) r<sub>2</sub> - r<sub>1</sub> =  \lambda  D) r<sub>2</sub> + r<sub>1</sub> =  \lambda /2 E) r<sub>2</sub> - r<sub>1</sub> =  \lambda /2 <div style=padding-top: 35px>  Two coherent sources of monochromatic light are located at S1 and S2 as shown. If the sources are in phase, the intensity at point P is a maximum when

A) d = λ\lambda
B) r2 + r1 = λ\lambda
C) r2 - r1 = λ\lambda
D) r2 + r1 = λ\lambda /2
E) r2 - r1 = λ\lambda /2
Question
Which, if any, of the following conditions is not necessary for the light waves from two sources to be coherent?

A) They must have the same frequency.
B) They must have the same amplitude.
C) They must have the same wavelength.
D) They must have a constant phase difference.
E) All of these conditions are necessary.
Question
Two side-by-side coherent light sources radiate at 450 nm. The phase difference between these two sources at a point in space is 0.333 radians. The path difference between the two sources could be

A) 15.8 nm
B) 20.3 nm
C) 23.8 nm
D) 29.7 nm
E) 32.1 nm
Question
Two side-by-side coherent light sources radiate at 600 nm. The phase difference between these two sources at a point in space is 0.582 radians. The path difference between the two sources could be

A) 43.5 nm
B) 55.6 nm
C) 62.4 nm
D) 75.9 nm
E) 87.4 nm
Question
The minimum path difference that will produce a phase difference of 90º for light of wavelength 500 nm is

A) 62.5 nm
B) 125 nm
C) 250 nm
D) 375 nm
E) 400 nm
Question
A phase shift of 180º occurs when a light wave

A) is transmitted through a boundary surface into a medium that is more dense than the medium from which the wave came.
B) is transmitted through a boundary surface into a medium that is less dense than the medium from which the wave came.
C) reflects from the boundary surface of a medium that is less dense than the medium in which the wave is traveling.
D) reflects from the boundary surface of a medium that is more dense than the medium in which the wave is traveling.
E) Both c and d are correct.
Question
Which of the following statements is true?

A) When two harmonic waves of the same frequency and wavelength but differing in phase combine, the resultant wave is a harmonic wave whose amplitude depends on the phase difference.
B) A phase difference between two waves can be the result of a difference in path length.
C) A path difference of one wavelength is equivalent to no phase difference at all.
D) A phase difference between two waves can be the result of reflection from a boundary surface.
E) All of these are correct.
Question
Diffraction of sound waves is more readily observable than that of light waves because

A) sound waves are longitudinal and not transverse.
B) sound waves have a higher frequency than light waves.
C) sound waves have a lower velocity than light waves.
D) sound waves have longer wavelengths than do light waves.
E) interference occurs more readily for longitudinal waves.
Question
Two side-by-side coherent light sources radiate at 480 nm. At a point in space where the path difference to these two sources is 50 nm, the phase difference could be

A) 0.238 radians
B) 0.375 radians
C) 0.466 radians
D) 0.582 radians
E) 0.654 radians
Question
For two identical rays of light to interfere destructively, their path lengths

A) must be equal.
B) must differ by an odd number of half wavelengths.
C) must differ by an even number of half wavelengths.
D) must differ by an integral number of wavelengths.
E) need not satisfy any of these conditions.
Question
You dip a wire loop into soapy water (n = 1.33) and hold it up vertically to look at the soap film in white light. The soap film looks dark at the top because it has sagged, and its thickness there is nearly zero, causing the reflected wavelengths to interfere destructively. Part way down the loop you see the first red band of the reflected white light. What is the thickness of the soap film there? (Take the wavelength of red light to be 680 nm.)

A) 130 nm
B) 170 nm
C) 220 nm
D) 250 nm
E) 340 nm
Question
 <strong>  A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately</strong> A) 7.1  \mu m B) 7.4  \mu m C) 6.5  \mu m D) 6.8  \mu m E) 7.8  \mu m <div style=padding-top: 35px>  A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately

A) 7.1 μ\mu m
B) 7.4 μ\mu m
C) 6.5 μ\mu m
D) 6.8 μ\mu m
E) 7.8 μ\mu m
Question
 <strong>  Two parallel glass plates of index of refraction n are separated by an air film of thickness d. Light of wavelength  \lambda  in air, normally incident on the plates, is intensified on reflection when, for some integer m</strong> A) 2d = m \lambda  B) 2d = m \lambda 0/n C) 2d = mn \lambda  D) 2d = (m + 1/2) \lambda  E) 2nd = m \lambda  /2 <div style=padding-top: 35px>  Two parallel glass plates of index of refraction n are separated by an air film of thickness d. Light of wavelength λ\lambda in air, normally incident on the plates, is intensified on reflection when, for some integer m

A) 2d = m λ\lambda
B) 2d = m λ\lambda 0/n
C) 2d = mn λ\lambda
D) 2d = (m + 1/2) λ\lambda
E) 2nd = m λ\lambda /2
Question
You deposit a thin film of magnesium difluoride on a glass lens (n > 1.60), reducing the reflection of yellow light, at normal incidence, to a minimum. You find that the thinnest coating that accomplishes this is 106 nm thick. The index of refraction for MgF2 for yellow light ( λ\lambda = 585 nm) is

A) 1.50
B) 1.38
C) 1.15
D) 1.00
E) 0.707
Question
Use the figure for the next two questions.  <strong>Use the figure for the next two questions.    -The interference pattern is from a convex lens placed on a flat reflecting surface using a monochromatic light of wavelength  \lambda  = 550 nm. The distance between the lens and the flat surface at position A is</strong> A) 275 nm B) 550 nm C) 687.5 nm D) 825 nm E) 962.5 nm <div style=padding-top: 35px>

-The interference pattern is from a convex lens placed on a flat reflecting surface using a monochromatic light of wavelength λ\lambda = 550 nm. The distance between the lens and the flat surface at position A is

A) 275 nm
B) 550 nm
C) 687.5 nm
D) 825 nm
E) 962.5 nm
Question
You create a wedge-shaped film of air between two flat plates of glass 2.5 cm wide by laying one on top of the other and placing a small slip of paper 1.0 mm thick between their edges at one end. You illuminate the glass plates with normally incident monochromatic light of unknown wavelength. Observing the reflection, you see dark fringes at both ends of the plates. Between the ends you see three other dark fringes. What is the wavelength of the incident light?

A) 250 nm
B) 400 nm
C) 440 nm
D) 500 nm
E) 620 nm
Question
You place a convex lens on top of a flat plate of glass and illuminate it with monochromatic light of wavelength 600 nm. You observe a dark circle at the center of the lens, surrounded by a series of concentric dark rings. What is the thickness of the air space between the lens and the flat glass plate where you see the sixth dark ring?

A) 3.90 µm
B) 3.60 µm
C) 1.80 µm
D) 1.95 µm
E) 2.10 µm
Question
 <strong>  Light of wave length \lambda is incident on two thin films that are in contact and surrounded by air. The top layer is  \lambda /4 thick and has an index of refraction of 1.33. The bottom layer is  \lambda /2 thick and has an index of refraction of 1.50. At normal incidence, the reflected rays that are in phase with each other are</strong> A) 1 and 2 B) 1 and 3 C) 2 and 3 D) 1, 2, and 3 E) None of these is correct. <div style=padding-top: 35px>  Light of wave length λ\lambda is incident on two thin films that are in contact and surrounded by air. The top layer is λ\lambda /4 thick and has an index of refraction of 1.33. The bottom layer is λ\lambda /2 thick and has an index of refraction of 1.50. At normal incidence, the reflected rays that are in phase with each other are

A) 1 and 2
B) 1 and 3
C) 2 and 3
D) 1, 2, and 3
E) None of these is correct.
Question
Use the figure for the next two questions.  <strong>Use the figure for the next two questions.    -The interference pattern is from a spherical lens placed on a flat reflecting surface using a monochromatic light of wavelength  \lambda  = 550 nm. If the distance from the center to A is 0.6 mm, the radius of curvature of the lens is</strong> A) 41.3 cm B) 82.5 cm C) 18.7 cm D) 37.4 cm E) 26.2 cm <div style=padding-top: 35px>

-The interference pattern is from a spherical lens placed on a flat reflecting surface using a monochromatic light of wavelength λ\lambda = 550 nm. If the distance from the center to A is 0.6 mm, the radius of curvature of the lens is

A) 41.3 cm
B) 82.5 cm
C) 18.7 cm
D) 37.4 cm
E) 26.2 cm
Question
You apply a material with n = 1.25 to a lens (ng = 1.5) to make a nonreflective coating due to destructive interference at a wavelength (in a vacuum) of 555 nm. What is the minimum thickness of the coating that you need?

A) 56 nm
B) 110 nm
C) 220 nm
D) 280 nm
E) 140 nm
Question
Light of wavelength 640 nm is incident perpendicularly from air onto a film 1000 nm thick and of 1.60 refractive index. When part of the light enters the film and is reflected back at the second face, the number of wavelengths contained along the path of this light in the film is

A) 1.0
B) 1.6
C) 2.0
D) 3.2
E) 5.0
Question
 <strong>  A broad spectrum of light ( \lambda  = 550 nm) illuminates normally a thin wedge of glass (n = 1.50). If the thick edge of the glass is 0.02 mm, the number of dark fringes observed is</strong> A) 109 B) 99 C) 73 D) 55 E) 33 <div style=padding-top: 35px>  A broad spectrum of light ( λ\lambda = 550 nm) illuminates normally a thin wedge of glass (n = 1.50). If the thick edge of the glass is 0.02 mm, the number of dark fringes observed is

A) 109
B) 99
C) 73
D) 55
E) 33
Question
You coat a glass lens (n = 1.65) with MgF2 (n = 1.38) to reduce reflection. The minimum thickness of coating required to produce destructive interference in reflected light whose wavelength in air is 560 nm is

A) 102 nm
B) 140 nm
C) 203 nm
D) 280 nm
E) None of these is correct.
Question
If we assume normal incidence, the minimum thickness of a soap film (n = 1.33) in air that gives constructive interference when viewed by reflected light of wavelength
400 nm is

A) 225 nm
B) 200 nm
C) 100 nm
D) 75 nm
E) 57 nm
Question
<strong>  The interference pattern is from a lens placed on a flat reflecting surface illuminate using a monochromatic light from above. From the pattern one can conclude that the lens</strong> A) is more curved on the left and right sides compared to top and bottom. B) is more curved on the top and bottom compared to the left and right sides. C) has a spherical surface. D) has a concave surface. E) none of the above <div style=padding-top: 35px> The interference pattern is from a lens placed on a flat reflecting surface illuminate using a monochromatic light from above. From the pattern one can conclude that the lens

A) is more curved on the left and right sides compared to top and bottom.
B) is more curved on the top and bottom compared to the left and right sides.
C) has a spherical surface.
D) has a concave surface.
E) none of the above
Question
A 3.5-cm-long microscope glass slide has one edge in contact with a flat plane of glass, while the other edge is slightly raised due to the insertion of a thin piece of paper. Sodium light of wavelength 589 nm is normally incident on the glass from above and interference fringes are observed by reflection with a regular spacing of 0.22 mm. Calculate the thickness of the piece of paper.

A) 9.4 * 10-5 m
B) 5.5 * 10-5 m
C) 2.4 *10-5 m
D) 4.7*10-5 m
E) None of these is correct.
Question
Two optically flat plates lie one on top of the other. A sheet of paper 0.1 mm thick is inserted between the plates at one edge. When the plates are illuminated by light of wavelength 589 nm, the number of interference fringes observed by reflected light is approximately

A) 470
B) 340
C) 294
D) 170
E) 123
Question
The different colors seen on a soap bubble are produced by

A) the dispersion of light by the water in the soap.
B) the interference of light reflected from the front and back of the soap film.
C) the different angles light strikes the surface of the soap film.
D) total internal reflection of light in the soap film.
E) None of the statements is correct.
Question
<strong>  A wedge-shaped film of air is formed by placing a glass plate on second flat glass plate. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. From the fringe pattern one can conclude that the surface of the first glass plate is</strong> A) much flatter than the wavelength used. B) flat on the left side but then has a concave to the right side. C) flat on the left side but then has a convex to the right side. D) flat on the right side but then has a concave to the left side. E) flat on the right side but then has a convex to the left side. <div style=padding-top: 35px> A wedge-shaped film of air is formed by placing a glass plate on second flat glass plate. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. From the fringe pattern one can conclude that the surface of the first glass plate is

A) much flatter than the wavelength used.
B) flat on the left side but then has a concave to the right side.
C) flat on the left side but then has a convex to the right side.
D) flat on the right side but then has a concave to the left side.
E) flat on the right side but then has a convex to the left side.
Question
At normal incidence, the minimum thickness of a soap film (n = 1.33) that causes constructive interference when viewed by reflected light of wavelength 400 nm is

A) 225 nm
B) 200 nm
C) 100 nm
D) 750 nm
E) 570 nm
Question
You set two parallel slits 0.1 mm apart at a distance of 2 m from a screen and illuminate them with light of wavelength 450 nm. The distance between a bright spot in the interference pattern and the dark spot adjacent to it is

A) 0.560 mm
B) 1.12 mm
C) 2.25 mm
D) 4.50 mm
E) 9.00 mm
Question
The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes near the center of the interference pattern

A) increases by a factor of 2.
B) increases by a factor of 4.
C) depends on the width of the slits.
D) decreases by a factor of 2.
E) decreases by a factor of 4.
Question
Two slits separated by 1.0 mm are illuminated with light of a single unknown wavelength. The tenth bright line from the central point of the interference pattern is observed to be at an angle of 0.34º. What is the wavelength of the light?

A) 620 nm
B) 590 nm
C) 560 nm
D) 450 nm
E) 600 nm
Question
In a double-slit experiment, the distance from the slits to the screen is decreased by a factor of 2. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes

A) increases by a factor of 2.
B) increases by a factor of 4.
C) depends on the width of the slits.
D) decreases by a factor of 2.
E) decreases by a factor of 4.
Question
You illuminate two slits 0.50 mm apart with light of wavelength 555 nm and observe interference fringes on a screen 6.0 m away. What is the spacing between the fringes on the screen?

A) 4.5 mm
B) 3.3 mm
C) 6.7 mm
D) 10 mm
E) 5.0 mm
Question
The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is about the same as the distance from the slits to the screen, the distance between adjacent fringes

A) increases by a factor of 2.
B) increases by a factor of 4.
C) decreases by a factor of 2.
D) decreases by a factor of 4.
E) depends on which two fringes are used for the measurement.
Question
You set two parallel slits 0.2 mm apart at a distance of 1 m from a screen and illuminate them with light of wavelength 600 nm. The distance between a bright spot in the interference pattern and the dark spot adjacent to it is

A) 0.375 mm
B) 0.750 mm
C) 1.50 mm
D) 3.00 mm
E) 6.00 mm
Question
In an experiment to demonstrate interference of light, it is essential that

A) coherent sources of light be used.
B) the light paths differ by not more than one-half wavelength.
C) the light be monochromatic.
D) the beam of light be a parallel beam.
E) there be no difference in light paths.
Question
Light of wavelength 500 nm illuminates parallel slits and produces an interference pattern on a screen that is 1 m from the slits. In terms of the initial intensity I0, the light's intensity in the interference pattern at a point for which the path difference is
100 nm is

A) 2.62 I0
B) 2.87 I0
C) 3.08 I0
D) 3.31 I0
E) 4.39 I0
Question
You set two parallel slits 0.2 mm apart at a distance of 1 m from a screen and illuminate them with light of wavelength 400 nm. The distance between the first and second dark lines of the interference pattern on the screen is

A) 2.5 mm
B) 2.0 mm
C) 1.5 mm
D) 1.0 mm
E) 0.5 mm
Question
<strong>  A narrow, horizontal slit is 0.50 mm above a horizontal plane mirror. The slit is illuminated by light of wavelength 400 nm. The interference pattern is viewed on a screen 10.0 m from the slit. What is the vertical distance from the mirror to the first bright line?</strong> A) 1.0 mm B) 2.0 mm C) 3.0 mm D) 4.0 mm E) 1.2 mm <div style=padding-top: 35px> A narrow, horizontal slit is 0.50 mm above a horizontal plane mirror. The slit is illuminated by light of wavelength 400 nm. The interference pattern is viewed on a screen 10.0 m from the slit. What is the vertical distance from the mirror to the first bright line?

A) 1.0 mm
B) 2.0 mm
C) 3.0 mm
D) 4.0 mm
E) 1.2 mm
Question
In order to produce several visible interference fringes from two narrow slits using light of a single wavelength, the distance between the slits must be of the order

A) of a few tenths of the wavelength.
B) of a few wavelengths.
C) of a few tens wavelengths.
D) of a few hundreds wavelengths.
E) The distance does not matter.
Question
When the slits in Young's experiment are moved closer together, the fringes

A) remains unchanged.
B) move closer together.
C) move further apart.
D) are less intense.
E) none of the above
Question
Two flat planes of glass are laid on top of one another. The upper plane is slightly raised due to the insertion of a thin piece of paper at one end and an air wedge is thus formed. Light of wavelength 500 nm is normally incident on the glass from above and interference fringes are observed by reflection with 2.5 fringes per cm. Calculate the angle of the wedge.

A) 6.3 * 10-5 deg
B) 1.8 * 10-3 deg
C) 4.0 * 10-4 deg
D) 3.6 * 10-3 deg
E) 5.7 * 10-4 deg
Question
If a thin soap film (n = 1.36) reflects predominately red light (about 680 nm), then what is the minimum thickness of the soap film?

A) 1.25 * 10-7 m
B) 6.80* 10-7 m
C) 2.50 * 10-7 m
D) 5.00 *10-7 m
E) None of these is correct.
Question
Light of wavelength 500 nm illuminates parallel slits and produces an interference pattern on a screen that is 1 m from the slits. In terms of the initial intensity I0, the light's intensity in the interference pattern at a point for which the path difference is
300 nm is

A) 0.262 I0
B) 0.382 I0
C) 0.447 I0
D) 0.581 I0
E) 0.629 I0
Question
In a double slit experiment, a very thin plate of glass of refractive index 1.58 is placed in the light path of one of the slit beams. When this was done, the center of the fringe pattern was displaced by 35 fringe widths. Calculate the thickness of the glass plate if the wavelength of light is 680 nm.

A) 4.1 * 10-5 m
B) 1.5 * 10-5 m
C) 3.0 * 10-5 m
D) 8.2 * 10-5 m
E) 3.8 * 10-5 m
Question
You set two slits 30 mm apart and 50 cm from a screen. When you illuminate the slits with light of wavelength 600 nm, the distance between the second and third dark interference lines is

A) 1.0 mm
B) 2.0 mm
C) 3.0 mm
D) 0.30 mm
E) 6.0 mm
Question
<strong>  Two narrow slits, their centers separated by 15 cm, are illuminated by monochromatic radiation and produce the pattern in the figure on a distant screen. The wavelength of the radiation is</strong> A) 0.52 cm B) 1.0 cm C) 1.6 cm D) 2.1 cm E) 3.0 cm <div style=padding-top: 35px> Two narrow slits, their centers separated by 15 cm, are illuminated by monochromatic radiation and produce the pattern in the figure on a distant screen. The wavelength of the radiation is

A) 0.52 cm
B) 1.0 cm
C) 1.6 cm
D) 2.1 cm
E) 3.0 cm
Question
Which of the following statements about Young's double-slit experiment is false?

A) The bands of light are caused by the interference of the light coming from the two slits.
B) The results of the double-slit experiment support the particle theory of light.
C) Double-slit interference patterns can also be produced with sound and water waves.
D) If the slits are moved closer together, the bands of light on the screen are spread farther apart.
E) The pattern of light on the screen consists of many bands, not just two bands.
Question
The pattern of light and dark fringes formed in Young's double-slit experiment is due to

A) interference and dispersion.
B) diffraction and refraction.
C) refraction and interference.
D) refraction and dispersion.
E) interference and diffraction.
Question
<strong>  The graphs are plots of relative intensities of various diffraction patterns versus the sine of the angle from the central maximum. The graph that represents the diffraction pattern from the widest single slit is</strong> A) 1 B) 2 C) 3 D) 4 E) 5 <div style=padding-top: 35px> The graphs are plots of relative intensities of various diffraction patterns versus the sine of the angle from the central maximum. The graph that represents the diffraction pattern from the widest single slit is

A) 1
B) 2
C) 3
D) 4
E) 5
Question
<strong>  Five coherent sources are used to produce an interference pattern. The phasor diagram shown could be used to calculate the intensity of the</strong> A) first minimum in the interference pattern. B) second maximum in an interference pattern. C) first maximum in an interference pattern. D) second minimum in an interference pattern. E) None of these is correct. <div style=padding-top: 35px> Five coherent sources are used to produce an interference pattern. The phasor diagram shown could be used to calculate the intensity of the

A) first minimum in the interference pattern.
B) second maximum in an interference pattern.
C) first maximum in an interference pattern.
D) second minimum in an interference pattern.
E) None of these is correct.
Question
<strong>  The interference and diffraction envelopes of a double slit are shown separately but to the same scale in the figure. For this arrangement, the number of fringes in the second diffraction maximum is</strong> A) 3 B) 4 C) 5 D) 7 E) 0 <div style=padding-top: 35px> The interference and diffraction envelopes of a double slit are shown separately but to the same scale in the figure. For this arrangement, the number of fringes in the second diffraction maximum is

A) 3
B) 4
C) 5
D) 7
E) 0
Question
<strong>  Which of the phasor diagrams shows the first minimum for five equally spaced in-phase sources?</strong> A) 1 B) 2 C) 3 D) 4 E) 5 <div style=padding-top: 35px> Which of the phasor diagrams shows the first minimum for five equally spaced in-phase sources?

A) 1
B) 2
C) 3
D) 4
E) 5
Question
Two slits of width a = 0.020 mm are separated by a distance d = 0.05 mm and illuminated by light of wavelength λ\lambda = 500 nm. The number of bright fringes seen in the central maximum is

A) 2.5
B) 3
C) 4
D) 5
E) 6
Question
In dealing with the diffraction pattern of a single slit, we are usually interested in the location of the first minimum in light intensity because

A) it is the only one that can be determined accurately.
B) it is the only one for which the small-angle approximation holds.
C) nearly all the light energy is contained in the central maximum.
D) it is the only one for which the location is directly proportional to the wavelength of the light.
E) it is the only one that can be described by Fraunhofer diffraction.
Question
The bending of light around an obstacle such as the edge of a slit is called

A) diffraction
B) dispersion
C) reflection
D) refraction
E) polarization
Question
Suppose you observe fifteen bright fringes in the central maximum of a double-slit interference pattern. If you know that the separation of the slits d = 0.01 mm, you can conclude that the width of each slit is

A) 0.63 mm
B) 1.25 mm
C) 1.68 mm
D) 1.88 mm
E) 1.99 mm
Question
Light of wavelength 650 nm is incident on a slit of width 25.0 µm. At what angle is the second diffraction minimum observed?

A) 0.052º
B) 1.5º
C) 2.2º
D) 3.0º
E) 3.7º
Question
<strong>  The fringes are the result of</strong> A) diffraction from a single slit. B) interference from a double slit in addition to diffraction from the two slits. C) interference from three slits. D) diffraction from three slits. E) None of these is correct. <div style=padding-top: 35px> The fringes are the result of

A) diffraction from a single slit.
B) interference from a double slit in addition to diffraction from the two slits.
C) interference from three slits.
D) diffraction from three slits.
E) None of these is correct.
Question
Suppose you observe nineteen bright fringes in the central maximum of a double-slit interference pattern. If you know that the separation of the slits d = 0.06 mm, you can conclude that the width of each slit is

A) 0.048 mm
B) 0.024 mm
C) 0.003 mm
D) 0.006 mm
E) 0.012 mm
Question
<strong>  Which of the following statements concerning the interference pattern described by the phasor diagram is true?</strong> A) There are exactly seven coherent sources. B) There is a relative minimum at the point in the pattern corresponding to the phasor diagram. C) The amplitude of the resultant wave at the point in the pattern corresponding to the phasor diagram is less than the amplitudes of the individual waves. D) The diagram corresponds to the third bright spot in the interference pattern. E) None of these is correct. <div style=padding-top: 35px> Which of the following statements concerning the interference pattern described by the phasor diagram is true?

A) There are exactly seven coherent sources.
B) There is a relative minimum at the point in the pattern corresponding to the phasor diagram.
C) The amplitude of the resultant wave at the point in the pattern corresponding to the phasor diagram is less than the amplitudes of the individual waves.
D) The diagram corresponds to the third bright spot in the interference pattern.
E) None of these is correct.
Question
<strong>  The diffraction pattern of a single slit is shown in the figure. The point at which the path difference of the extreme rays is two wavelengths is</strong> A) 1 B) 2 C) 3 D) 4 E) 5 <div style=padding-top: 35px> The diffraction pattern of a single slit is shown in the figure. The point at which the path difference of the extreme rays is two wavelengths is

A) 1
B) 2
C) 3
D) 4
E) 5
Question
Two slits of width a = 0.0016 mm are separated by a distance d = 0.04 mm and illuminated by light of wavelength λ\lambda = 450 nm. The number of bright fringes seen in the central maximum is

A) 8
B) 16
C) 25
D) 37
E) 49
Question
A single-slit diffraction pattern is displayed on a screen 0.900 m away from the slit. If the wavelength of the light is 600 nm and the slit is 1.50 * 10-4 m wide, the distance from the first minimum on the right to the first minimum on the left is

A) 0.164 mm
B) 1.83 mm
C) 3.99 mm
D) 7.20 mm
E) 7.98 mm
Question
As the width of the slit producing a single-slit diffraction pattern is slowly and steadily reduced (always remaining larger than the wavelength of the light), the diffraction pattern

A) slowly and steadily gets wider.
B) slowly and steadily gets brighter.
C) does not change because the wavelength of the light does not change.
D) slowly and steadily gets narrower.
E) None of these is correct.
Question
When a parallel beam of light is diffracted at a single slit,

A) the shadow is always sharp.
B) the narrower the slit, the narrower the central diffraction maximum.
C) the narrower the slit, the wider the central diffraction maximum.
D) the width of the central diffraction maximum is independent of the width of the slit.
E) None of these is correct.
Question
Light of wavelength 450 nm is incident on a narrow slit. The diffraction pattern is observed on a screen 5.0 m from the slit, and the central maximum is observed to have a width of 22 cm. What is the width of the slit?

A) 4.5 µm
B) 5.0 µm
C) 10 µm
D) 20 µm
E) 0.20 µm
Question
An easy way to distinguish whether the fringe pattern is the result of a single slit or from a double slit is

A) the intensity for each fringe is much stronger for a single slit than a double slit.
B) the intensity for each fringe is much stronger for a double slit than a single slit.
C) the width central maximum from a single slit is twice as width as the other wide whereas the widths of the fringes from a double slit are about the same width.
D) that there are many more fringes from a single slit than a double slit.
E) that there are many more fringes from a double slit than a single slit.
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Deck 13: Interference and Diffraction
1
Two waves, one with amplitude A and the second with amplitude 2A, are out of phase by 180 °\degree . The resultant intensity is

A) zero
B) A
C) A2
D) 2A2
E) (3A)2
A2
2
<strong>  In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is</strong> A) 1 only B) 2 only C) 3 only D) 1 and 2 E) 2 and 3 In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is

A) 1 only
B) 2 only
C) 3 only
D) 1 and 2
E) 2 and 3
1 only
3
 <strong>  The phase difference for the two waves shown in the figure is</strong> A) 2  \pi  B)   \pi  C) 3  \pi /2 D)   \pi /2 E) It is not possible to answer this question without additional information.  The phase difference for the two waves shown in the figure is

A) 2 π\pi
B) π\pi
C) 3 π\pi /2
D) π\pi /2
E) It is not possible to answer this question without additional information.
π\pi /2
4
Two waves, one with amplitude A and the second with amplitude 2A, are in phase. The resultant intensity is

A) zero
B) A
C) 3A
D) 3A2
E) (3A)2
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5
Visible light from an ordinary source such as a sodium lamp can be used to produce interference effects that demonstrate the wave nature of light, provided that

A) the light beam from the single source is split into two (or more) beams that have a constant phase relationship to one another.
B) the light is polarized.
C) the light is not polarized.
D) Interference effects cannot be demonstrated with ordinary light sources.
E) None of these conditions are satisfied.
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6
For us to see interference phenomena in a thin film,

A) the incoming light must be monochromatic.
B) the index of refraction of the thin film must be greater than the index of refraction of the material below it.
C) the index of refraction of the thin film must be less than the index of refraction of the material below it.
D) the incoming light must be multicolored.
E) none of these conditions need exist
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7
The minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is

A) 600 nm
B) 500 nm
C) 300 nm
D) 200 nm
E) 100 nm
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8
 <strong>  The path difference for the two waves shown in the figure could be</strong> A) ¾ \lambda  B) ½ \lambda  C) ¼ \lambda  D) \lambda  E) It is not possible to answer this question without additional information.  The path difference for the two waves shown in the figure could be

A) ¾ λ\lambda
B) ½ λ\lambda
C) ¼ λ\lambda
D) λ\lambda
E) It is not possible to answer this question without additional information.
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9
Two side-by-side coherent light sources radiate at 633 nm. At a point in space where the path difference to these two sources is 30 nm, the phase difference could be

A) 0.238 radians
B) 0.298 radians
C) 0.324 radians
D) 0.356 radians
E) 0.429 radians
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10
 <strong>  Why are fringes not observed if the angle of the wedge of air in the diagram is too large?</strong> A) For a large angle, the small-angle approximation (sin  \theta   \approx   \theta ) is not valid. B) the light passing through the wedge of air loses its coherence C) the fringes overlap D) the fringes are too close together to be seen individually E) None of these is correct.  Why are fringes not observed if the angle of the wedge of air in the diagram is too large?

A) For a large angle, the small-angle approximation (sin θ\theta \approx θ\theta ) is not valid.
B) the light passing through the wedge of air loses its coherence
C) the fringes overlap
D) the fringes are too close together to be seen individually
E) None of these is correct.
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11
 <strong>  Two coherent sources of monochromatic light are located at S<sub>1</sub> and S<sub>2</sub> as shown. If the sources are in phase, the intensity at point P is a maximum when</strong> A) d = \lambda  B) r<sub>2</sub> + r<sub>1</sub> =  \lambda  C) r<sub>2</sub> - r<sub>1</sub> =  \lambda  D) r<sub>2</sub> + r<sub>1</sub> =  \lambda /2 E) r<sub>2</sub> - r<sub>1</sub> =  \lambda /2  Two coherent sources of monochromatic light are located at S1 and S2 as shown. If the sources are in phase, the intensity at point P is a maximum when

A) d = λ\lambda
B) r2 + r1 = λ\lambda
C) r2 - r1 = λ\lambda
D) r2 + r1 = λ\lambda /2
E) r2 - r1 = λ\lambda /2
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12
Which, if any, of the following conditions is not necessary for the light waves from two sources to be coherent?

A) They must have the same frequency.
B) They must have the same amplitude.
C) They must have the same wavelength.
D) They must have a constant phase difference.
E) All of these conditions are necessary.
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13
Two side-by-side coherent light sources radiate at 450 nm. The phase difference between these two sources at a point in space is 0.333 radians. The path difference between the two sources could be

A) 15.8 nm
B) 20.3 nm
C) 23.8 nm
D) 29.7 nm
E) 32.1 nm
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14
Two side-by-side coherent light sources radiate at 600 nm. The phase difference between these two sources at a point in space is 0.582 radians. The path difference between the two sources could be

A) 43.5 nm
B) 55.6 nm
C) 62.4 nm
D) 75.9 nm
E) 87.4 nm
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15
The minimum path difference that will produce a phase difference of 90º for light of wavelength 500 nm is

A) 62.5 nm
B) 125 nm
C) 250 nm
D) 375 nm
E) 400 nm
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16
A phase shift of 180º occurs when a light wave

A) is transmitted through a boundary surface into a medium that is more dense than the medium from which the wave came.
B) is transmitted through a boundary surface into a medium that is less dense than the medium from which the wave came.
C) reflects from the boundary surface of a medium that is less dense than the medium in which the wave is traveling.
D) reflects from the boundary surface of a medium that is more dense than the medium in which the wave is traveling.
E) Both c and d are correct.
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17
Which of the following statements is true?

A) When two harmonic waves of the same frequency and wavelength but differing in phase combine, the resultant wave is a harmonic wave whose amplitude depends on the phase difference.
B) A phase difference between two waves can be the result of a difference in path length.
C) A path difference of one wavelength is equivalent to no phase difference at all.
D) A phase difference between two waves can be the result of reflection from a boundary surface.
E) All of these are correct.
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18
Diffraction of sound waves is more readily observable than that of light waves because

A) sound waves are longitudinal and not transverse.
B) sound waves have a higher frequency than light waves.
C) sound waves have a lower velocity than light waves.
D) sound waves have longer wavelengths than do light waves.
E) interference occurs more readily for longitudinal waves.
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19
Two side-by-side coherent light sources radiate at 480 nm. At a point in space where the path difference to these two sources is 50 nm, the phase difference could be

A) 0.238 radians
B) 0.375 radians
C) 0.466 radians
D) 0.582 radians
E) 0.654 radians
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20
For two identical rays of light to interfere destructively, their path lengths

A) must be equal.
B) must differ by an odd number of half wavelengths.
C) must differ by an even number of half wavelengths.
D) must differ by an integral number of wavelengths.
E) need not satisfy any of these conditions.
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21
You dip a wire loop into soapy water (n = 1.33) and hold it up vertically to look at the soap film in white light. The soap film looks dark at the top because it has sagged, and its thickness there is nearly zero, causing the reflected wavelengths to interfere destructively. Part way down the loop you see the first red band of the reflected white light. What is the thickness of the soap film there? (Take the wavelength of red light to be 680 nm.)

A) 130 nm
B) 170 nm
C) 220 nm
D) 250 nm
E) 340 nm
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22
 <strong>  A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately</strong> A) 7.1  \mu m B) 7.4  \mu m C) 6.5  \mu m D) 6.8  \mu m E) 7.8  \mu m  A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately

A) 7.1 μ\mu m
B) 7.4 μ\mu m
C) 6.5 μ\mu m
D) 6.8 μ\mu m
E) 7.8 μ\mu m
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23
 <strong>  Two parallel glass plates of index of refraction n are separated by an air film of thickness d. Light of wavelength  \lambda  in air, normally incident on the plates, is intensified on reflection when, for some integer m</strong> A) 2d = m \lambda  B) 2d = m \lambda 0/n C) 2d = mn \lambda  D) 2d = (m + 1/2) \lambda  E) 2nd = m \lambda  /2  Two parallel glass plates of index of refraction n are separated by an air film of thickness d. Light of wavelength λ\lambda in air, normally incident on the plates, is intensified on reflection when, for some integer m

A) 2d = m λ\lambda
B) 2d = m λ\lambda 0/n
C) 2d = mn λ\lambda
D) 2d = (m + 1/2) λ\lambda
E) 2nd = m λ\lambda /2
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24
You deposit a thin film of magnesium difluoride on a glass lens (n > 1.60), reducing the reflection of yellow light, at normal incidence, to a minimum. You find that the thinnest coating that accomplishes this is 106 nm thick. The index of refraction for MgF2 for yellow light ( λ\lambda = 585 nm) is

A) 1.50
B) 1.38
C) 1.15
D) 1.00
E) 0.707
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25
Use the figure for the next two questions.  <strong>Use the figure for the next two questions.    -The interference pattern is from a convex lens placed on a flat reflecting surface using a monochromatic light of wavelength  \lambda  = 550 nm. The distance between the lens and the flat surface at position A is</strong> A) 275 nm B) 550 nm C) 687.5 nm D) 825 nm E) 962.5 nm

-The interference pattern is from a convex lens placed on a flat reflecting surface using a monochromatic light of wavelength λ\lambda = 550 nm. The distance between the lens and the flat surface at position A is

A) 275 nm
B) 550 nm
C) 687.5 nm
D) 825 nm
E) 962.5 nm
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26
You create a wedge-shaped film of air between two flat plates of glass 2.5 cm wide by laying one on top of the other and placing a small slip of paper 1.0 mm thick between their edges at one end. You illuminate the glass plates with normally incident monochromatic light of unknown wavelength. Observing the reflection, you see dark fringes at both ends of the plates. Between the ends you see three other dark fringes. What is the wavelength of the incident light?

A) 250 nm
B) 400 nm
C) 440 nm
D) 500 nm
E) 620 nm
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27
You place a convex lens on top of a flat plate of glass and illuminate it with monochromatic light of wavelength 600 nm. You observe a dark circle at the center of the lens, surrounded by a series of concentric dark rings. What is the thickness of the air space between the lens and the flat glass plate where you see the sixth dark ring?

A) 3.90 µm
B) 3.60 µm
C) 1.80 µm
D) 1.95 µm
E) 2.10 µm
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28
 <strong>  Light of wave length \lambda is incident on two thin films that are in contact and surrounded by air. The top layer is  \lambda /4 thick and has an index of refraction of 1.33. The bottom layer is  \lambda /2 thick and has an index of refraction of 1.50. At normal incidence, the reflected rays that are in phase with each other are</strong> A) 1 and 2 B) 1 and 3 C) 2 and 3 D) 1, 2, and 3 E) None of these is correct.  Light of wave length λ\lambda is incident on two thin films that are in contact and surrounded by air. The top layer is λ\lambda /4 thick and has an index of refraction of 1.33. The bottom layer is λ\lambda /2 thick and has an index of refraction of 1.50. At normal incidence, the reflected rays that are in phase with each other are

A) 1 and 2
B) 1 and 3
C) 2 and 3
D) 1, 2, and 3
E) None of these is correct.
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29
Use the figure for the next two questions.  <strong>Use the figure for the next two questions.    -The interference pattern is from a spherical lens placed on a flat reflecting surface using a monochromatic light of wavelength  \lambda  = 550 nm. If the distance from the center to A is 0.6 mm, the radius of curvature of the lens is</strong> A) 41.3 cm B) 82.5 cm C) 18.7 cm D) 37.4 cm E) 26.2 cm

-The interference pattern is from a spherical lens placed on a flat reflecting surface using a monochromatic light of wavelength λ\lambda = 550 nm. If the distance from the center to A is 0.6 mm, the radius of curvature of the lens is

A) 41.3 cm
B) 82.5 cm
C) 18.7 cm
D) 37.4 cm
E) 26.2 cm
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30
You apply a material with n = 1.25 to a lens (ng = 1.5) to make a nonreflective coating due to destructive interference at a wavelength (in a vacuum) of 555 nm. What is the minimum thickness of the coating that you need?

A) 56 nm
B) 110 nm
C) 220 nm
D) 280 nm
E) 140 nm
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31
Light of wavelength 640 nm is incident perpendicularly from air onto a film 1000 nm thick and of 1.60 refractive index. When part of the light enters the film and is reflected back at the second face, the number of wavelengths contained along the path of this light in the film is

A) 1.0
B) 1.6
C) 2.0
D) 3.2
E) 5.0
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32
 <strong>  A broad spectrum of light ( \lambda  = 550 nm) illuminates normally a thin wedge of glass (n = 1.50). If the thick edge of the glass is 0.02 mm, the number of dark fringes observed is</strong> A) 109 B) 99 C) 73 D) 55 E) 33  A broad spectrum of light ( λ\lambda = 550 nm) illuminates normally a thin wedge of glass (n = 1.50). If the thick edge of the glass is 0.02 mm, the number of dark fringes observed is

A) 109
B) 99
C) 73
D) 55
E) 33
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33
You coat a glass lens (n = 1.65) with MgF2 (n = 1.38) to reduce reflection. The minimum thickness of coating required to produce destructive interference in reflected light whose wavelength in air is 560 nm is

A) 102 nm
B) 140 nm
C) 203 nm
D) 280 nm
E) None of these is correct.
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34
If we assume normal incidence, the minimum thickness of a soap film (n = 1.33) in air that gives constructive interference when viewed by reflected light of wavelength
400 nm is

A) 225 nm
B) 200 nm
C) 100 nm
D) 75 nm
E) 57 nm
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35
<strong>  The interference pattern is from a lens placed on a flat reflecting surface illuminate using a monochromatic light from above. From the pattern one can conclude that the lens</strong> A) is more curved on the left and right sides compared to top and bottom. B) is more curved on the top and bottom compared to the left and right sides. C) has a spherical surface. D) has a concave surface. E) none of the above The interference pattern is from a lens placed on a flat reflecting surface illuminate using a monochromatic light from above. From the pattern one can conclude that the lens

A) is more curved on the left and right sides compared to top and bottom.
B) is more curved on the top and bottom compared to the left and right sides.
C) has a spherical surface.
D) has a concave surface.
E) none of the above
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36
A 3.5-cm-long microscope glass slide has one edge in contact with a flat plane of glass, while the other edge is slightly raised due to the insertion of a thin piece of paper. Sodium light of wavelength 589 nm is normally incident on the glass from above and interference fringes are observed by reflection with a regular spacing of 0.22 mm. Calculate the thickness of the piece of paper.

A) 9.4 * 10-5 m
B) 5.5 * 10-5 m
C) 2.4 *10-5 m
D) 4.7*10-5 m
E) None of these is correct.
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37
Two optically flat plates lie one on top of the other. A sheet of paper 0.1 mm thick is inserted between the plates at one edge. When the plates are illuminated by light of wavelength 589 nm, the number of interference fringes observed by reflected light is approximately

A) 470
B) 340
C) 294
D) 170
E) 123
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38
The different colors seen on a soap bubble are produced by

A) the dispersion of light by the water in the soap.
B) the interference of light reflected from the front and back of the soap film.
C) the different angles light strikes the surface of the soap film.
D) total internal reflection of light in the soap film.
E) None of the statements is correct.
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39
<strong>  A wedge-shaped film of air is formed by placing a glass plate on second flat glass plate. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. From the fringe pattern one can conclude that the surface of the first glass plate is</strong> A) much flatter than the wavelength used. B) flat on the left side but then has a concave to the right side. C) flat on the left side but then has a convex to the right side. D) flat on the right side but then has a concave to the left side. E) flat on the right side but then has a convex to the left side. A wedge-shaped film of air is formed by placing a glass plate on second flat glass plate. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. From the fringe pattern one can conclude that the surface of the first glass plate is

A) much flatter than the wavelength used.
B) flat on the left side but then has a concave to the right side.
C) flat on the left side but then has a convex to the right side.
D) flat on the right side but then has a concave to the left side.
E) flat on the right side but then has a convex to the left side.
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40
At normal incidence, the minimum thickness of a soap film (n = 1.33) that causes constructive interference when viewed by reflected light of wavelength 400 nm is

A) 225 nm
B) 200 nm
C) 100 nm
D) 750 nm
E) 570 nm
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41
You set two parallel slits 0.1 mm apart at a distance of 2 m from a screen and illuminate them with light of wavelength 450 nm. The distance between a bright spot in the interference pattern and the dark spot adjacent to it is

A) 0.560 mm
B) 1.12 mm
C) 2.25 mm
D) 4.50 mm
E) 9.00 mm
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42
The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes near the center of the interference pattern

A) increases by a factor of 2.
B) increases by a factor of 4.
C) depends on the width of the slits.
D) decreases by a factor of 2.
E) decreases by a factor of 4.
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43
Two slits separated by 1.0 mm are illuminated with light of a single unknown wavelength. The tenth bright line from the central point of the interference pattern is observed to be at an angle of 0.34º. What is the wavelength of the light?

A) 620 nm
B) 590 nm
C) 560 nm
D) 450 nm
E) 600 nm
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44
In a double-slit experiment, the distance from the slits to the screen is decreased by a factor of 2. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes

A) increases by a factor of 2.
B) increases by a factor of 4.
C) depends on the width of the slits.
D) decreases by a factor of 2.
E) decreases by a factor of 4.
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45
You illuminate two slits 0.50 mm apart with light of wavelength 555 nm and observe interference fringes on a screen 6.0 m away. What is the spacing between the fringes on the screen?

A) 4.5 mm
B) 3.3 mm
C) 6.7 mm
D) 10 mm
E) 5.0 mm
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46
The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is about the same as the distance from the slits to the screen, the distance between adjacent fringes

A) increases by a factor of 2.
B) increases by a factor of 4.
C) decreases by a factor of 2.
D) decreases by a factor of 4.
E) depends on which two fringes are used for the measurement.
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47
You set two parallel slits 0.2 mm apart at a distance of 1 m from a screen and illuminate them with light of wavelength 600 nm. The distance between a bright spot in the interference pattern and the dark spot adjacent to it is

A) 0.375 mm
B) 0.750 mm
C) 1.50 mm
D) 3.00 mm
E) 6.00 mm
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48
In an experiment to demonstrate interference of light, it is essential that

A) coherent sources of light be used.
B) the light paths differ by not more than one-half wavelength.
C) the light be monochromatic.
D) the beam of light be a parallel beam.
E) there be no difference in light paths.
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49
Light of wavelength 500 nm illuminates parallel slits and produces an interference pattern on a screen that is 1 m from the slits. In terms of the initial intensity I0, the light's intensity in the interference pattern at a point for which the path difference is
100 nm is

A) 2.62 I0
B) 2.87 I0
C) 3.08 I0
D) 3.31 I0
E) 4.39 I0
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50
You set two parallel slits 0.2 mm apart at a distance of 1 m from a screen and illuminate them with light of wavelength 400 nm. The distance between the first and second dark lines of the interference pattern on the screen is

A) 2.5 mm
B) 2.0 mm
C) 1.5 mm
D) 1.0 mm
E) 0.5 mm
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51
<strong>  A narrow, horizontal slit is 0.50 mm above a horizontal plane mirror. The slit is illuminated by light of wavelength 400 nm. The interference pattern is viewed on a screen 10.0 m from the slit. What is the vertical distance from the mirror to the first bright line?</strong> A) 1.0 mm B) 2.0 mm C) 3.0 mm D) 4.0 mm E) 1.2 mm A narrow, horizontal slit is 0.50 mm above a horizontal plane mirror. The slit is illuminated by light of wavelength 400 nm. The interference pattern is viewed on a screen 10.0 m from the slit. What is the vertical distance from the mirror to the first bright line?

A) 1.0 mm
B) 2.0 mm
C) 3.0 mm
D) 4.0 mm
E) 1.2 mm
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52
In order to produce several visible interference fringes from two narrow slits using light of a single wavelength, the distance between the slits must be of the order

A) of a few tenths of the wavelength.
B) of a few wavelengths.
C) of a few tens wavelengths.
D) of a few hundreds wavelengths.
E) The distance does not matter.
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53
When the slits in Young's experiment are moved closer together, the fringes

A) remains unchanged.
B) move closer together.
C) move further apart.
D) are less intense.
E) none of the above
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54
Two flat planes of glass are laid on top of one another. The upper plane is slightly raised due to the insertion of a thin piece of paper at one end and an air wedge is thus formed. Light of wavelength 500 nm is normally incident on the glass from above and interference fringes are observed by reflection with 2.5 fringes per cm. Calculate the angle of the wedge.

A) 6.3 * 10-5 deg
B) 1.8 * 10-3 deg
C) 4.0 * 10-4 deg
D) 3.6 * 10-3 deg
E) 5.7 * 10-4 deg
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55
If a thin soap film (n = 1.36) reflects predominately red light (about 680 nm), then what is the minimum thickness of the soap film?

A) 1.25 * 10-7 m
B) 6.80* 10-7 m
C) 2.50 * 10-7 m
D) 5.00 *10-7 m
E) None of these is correct.
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56
Light of wavelength 500 nm illuminates parallel slits and produces an interference pattern on a screen that is 1 m from the slits. In terms of the initial intensity I0, the light's intensity in the interference pattern at a point for which the path difference is
300 nm is

A) 0.262 I0
B) 0.382 I0
C) 0.447 I0
D) 0.581 I0
E) 0.629 I0
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57
In a double slit experiment, a very thin plate of glass of refractive index 1.58 is placed in the light path of one of the slit beams. When this was done, the center of the fringe pattern was displaced by 35 fringe widths. Calculate the thickness of the glass plate if the wavelength of light is 680 nm.

A) 4.1 * 10-5 m
B) 1.5 * 10-5 m
C) 3.0 * 10-5 m
D) 8.2 * 10-5 m
E) 3.8 * 10-5 m
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58
You set two slits 30 mm apart and 50 cm from a screen. When you illuminate the slits with light of wavelength 600 nm, the distance between the second and third dark interference lines is

A) 1.0 mm
B) 2.0 mm
C) 3.0 mm
D) 0.30 mm
E) 6.0 mm
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59
<strong>  Two narrow slits, their centers separated by 15 cm, are illuminated by monochromatic radiation and produce the pattern in the figure on a distant screen. The wavelength of the radiation is</strong> A) 0.52 cm B) 1.0 cm C) 1.6 cm D) 2.1 cm E) 3.0 cm Two narrow slits, their centers separated by 15 cm, are illuminated by monochromatic radiation and produce the pattern in the figure on a distant screen. The wavelength of the radiation is

A) 0.52 cm
B) 1.0 cm
C) 1.6 cm
D) 2.1 cm
E) 3.0 cm
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60
Which of the following statements about Young's double-slit experiment is false?

A) The bands of light are caused by the interference of the light coming from the two slits.
B) The results of the double-slit experiment support the particle theory of light.
C) Double-slit interference patterns can also be produced with sound and water waves.
D) If the slits are moved closer together, the bands of light on the screen are spread farther apart.
E) The pattern of light on the screen consists of many bands, not just two bands.
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61
The pattern of light and dark fringes formed in Young's double-slit experiment is due to

A) interference and dispersion.
B) diffraction and refraction.
C) refraction and interference.
D) refraction and dispersion.
E) interference and diffraction.
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62
<strong>  The graphs are plots of relative intensities of various diffraction patterns versus the sine of the angle from the central maximum. The graph that represents the diffraction pattern from the widest single slit is</strong> A) 1 B) 2 C) 3 D) 4 E) 5 The graphs are plots of relative intensities of various diffraction patterns versus the sine of the angle from the central maximum. The graph that represents the diffraction pattern from the widest single slit is

A) 1
B) 2
C) 3
D) 4
E) 5
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63
<strong>  Five coherent sources are used to produce an interference pattern. The phasor diagram shown could be used to calculate the intensity of the</strong> A) first minimum in the interference pattern. B) second maximum in an interference pattern. C) first maximum in an interference pattern. D) second minimum in an interference pattern. E) None of these is correct. Five coherent sources are used to produce an interference pattern. The phasor diagram shown could be used to calculate the intensity of the

A) first minimum in the interference pattern.
B) second maximum in an interference pattern.
C) first maximum in an interference pattern.
D) second minimum in an interference pattern.
E) None of these is correct.
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64
<strong>  The interference and diffraction envelopes of a double slit are shown separately but to the same scale in the figure. For this arrangement, the number of fringes in the second diffraction maximum is</strong> A) 3 B) 4 C) 5 D) 7 E) 0 The interference and diffraction envelopes of a double slit are shown separately but to the same scale in the figure. For this arrangement, the number of fringes in the second diffraction maximum is

A) 3
B) 4
C) 5
D) 7
E) 0
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65
<strong>  Which of the phasor diagrams shows the first minimum for five equally spaced in-phase sources?</strong> A) 1 B) 2 C) 3 D) 4 E) 5 Which of the phasor diagrams shows the first minimum for five equally spaced in-phase sources?

A) 1
B) 2
C) 3
D) 4
E) 5
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66
Two slits of width a = 0.020 mm are separated by a distance d = 0.05 mm and illuminated by light of wavelength λ\lambda = 500 nm. The number of bright fringes seen in the central maximum is

A) 2.5
B) 3
C) 4
D) 5
E) 6
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67
In dealing with the diffraction pattern of a single slit, we are usually interested in the location of the first minimum in light intensity because

A) it is the only one that can be determined accurately.
B) it is the only one for which the small-angle approximation holds.
C) nearly all the light energy is contained in the central maximum.
D) it is the only one for which the location is directly proportional to the wavelength of the light.
E) it is the only one that can be described by Fraunhofer diffraction.
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68
The bending of light around an obstacle such as the edge of a slit is called

A) diffraction
B) dispersion
C) reflection
D) refraction
E) polarization
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69
Suppose you observe fifteen bright fringes in the central maximum of a double-slit interference pattern. If you know that the separation of the slits d = 0.01 mm, you can conclude that the width of each slit is

A) 0.63 mm
B) 1.25 mm
C) 1.68 mm
D) 1.88 mm
E) 1.99 mm
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70
Light of wavelength 650 nm is incident on a slit of width 25.0 µm. At what angle is the second diffraction minimum observed?

A) 0.052º
B) 1.5º
C) 2.2º
D) 3.0º
E) 3.7º
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71
<strong>  The fringes are the result of</strong> A) diffraction from a single slit. B) interference from a double slit in addition to diffraction from the two slits. C) interference from three slits. D) diffraction from three slits. E) None of these is correct. The fringes are the result of

A) diffraction from a single slit.
B) interference from a double slit in addition to diffraction from the two slits.
C) interference from three slits.
D) diffraction from three slits.
E) None of these is correct.
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72
Suppose you observe nineteen bright fringes in the central maximum of a double-slit interference pattern. If you know that the separation of the slits d = 0.06 mm, you can conclude that the width of each slit is

A) 0.048 mm
B) 0.024 mm
C) 0.003 mm
D) 0.006 mm
E) 0.012 mm
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73
<strong>  Which of the following statements concerning the interference pattern described by the phasor diagram is true?</strong> A) There are exactly seven coherent sources. B) There is a relative minimum at the point in the pattern corresponding to the phasor diagram. C) The amplitude of the resultant wave at the point in the pattern corresponding to the phasor diagram is less than the amplitudes of the individual waves. D) The diagram corresponds to the third bright spot in the interference pattern. E) None of these is correct. Which of the following statements concerning the interference pattern described by the phasor diagram is true?

A) There are exactly seven coherent sources.
B) There is a relative minimum at the point in the pattern corresponding to the phasor diagram.
C) The amplitude of the resultant wave at the point in the pattern corresponding to the phasor diagram is less than the amplitudes of the individual waves.
D) The diagram corresponds to the third bright spot in the interference pattern.
E) None of these is correct.
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74
<strong>  The diffraction pattern of a single slit is shown in the figure. The point at which the path difference of the extreme rays is two wavelengths is</strong> A) 1 B) 2 C) 3 D) 4 E) 5 The diffraction pattern of a single slit is shown in the figure. The point at which the path difference of the extreme rays is two wavelengths is

A) 1
B) 2
C) 3
D) 4
E) 5
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75
Two slits of width a = 0.0016 mm are separated by a distance d = 0.04 mm and illuminated by light of wavelength λ\lambda = 450 nm. The number of bright fringes seen in the central maximum is

A) 8
B) 16
C) 25
D) 37
E) 49
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76
A single-slit diffraction pattern is displayed on a screen 0.900 m away from the slit. If the wavelength of the light is 600 nm and the slit is 1.50 * 10-4 m wide, the distance from the first minimum on the right to the first minimum on the left is

A) 0.164 mm
B) 1.83 mm
C) 3.99 mm
D) 7.20 mm
E) 7.98 mm
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77
As the width of the slit producing a single-slit diffraction pattern is slowly and steadily reduced (always remaining larger than the wavelength of the light), the diffraction pattern

A) slowly and steadily gets wider.
B) slowly and steadily gets brighter.
C) does not change because the wavelength of the light does not change.
D) slowly and steadily gets narrower.
E) None of these is correct.
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78
When a parallel beam of light is diffracted at a single slit,

A) the shadow is always sharp.
B) the narrower the slit, the narrower the central diffraction maximum.
C) the narrower the slit, the wider the central diffraction maximum.
D) the width of the central diffraction maximum is independent of the width of the slit.
E) None of these is correct.
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79
Light of wavelength 450 nm is incident on a narrow slit. The diffraction pattern is observed on a screen 5.0 m from the slit, and the central maximum is observed to have a width of 22 cm. What is the width of the slit?

A) 4.5 µm
B) 5.0 µm
C) 10 µm
D) 20 µm
E) 0.20 µm
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80
An easy way to distinguish whether the fringe pattern is the result of a single slit or from a double slit is

A) the intensity for each fringe is much stronger for a single slit than a double slit.
B) the intensity for each fringe is much stronger for a double slit than a single slit.
C) the width central maximum from a single slit is twice as width as the other wide whereas the widths of the fringes from a double slit are about the same width.
D) that there are many more fringes from a single slit than a double slit.
E) that there are many more fringes from a double slit than a single slit.
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