Deck 33: Interference and Diffraction

Question 1

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

Answer 1

300 nm

Question 2

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.

Answer 2

They must have the same amplitude.

Question 3

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

Answer 3

1.80 µm

Question 4

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 5

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 6

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 7

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 8

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 9

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 10

Two waves,one with amplitude A and the second with amplitude 2A,are out of phase by 180 ^$\circ$ .The resultant intensity is

A)zero
B)A
C)A²
D)2A²
E)(3A)²

Question 11

You apply a material with n = 1.25 to a lens (n_g = 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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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 21

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 $\times$ 10^-5 deg
B)1.8 $\times$ 10^-3 deg
C)4.0 $\times$ 10^-4 deg
D)3.6 $\times$ 10^-3 deg
E)5.7 $\times$ 10^-4 deg

Question 22

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 23

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 ( $\lambda$ = 585 nm)is

A)1.50
B)1.38
C)1.15
D)1.00
E)0.707

Question 24

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

A)41.3 cm
B)82.5 cm
C)18.7 cm
D)37.4 cm
E)26.2 cm

Question 25

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 26

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 27

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 28

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 $\times$ 10^-7 m
B)6.80 $\times$ 10^-7 m
C)2.50 $\times$ 10^-7 m
D)5.00 $\times$ 10^-7 m
E)None of these is correct.

Question 29

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 30

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 31

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 32

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

A)275 nm
B)550 nm
C)687.5 nm
D)825 nm
E)962.5 nm

Question 33

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 $\times$ 10^-5 m
B)5.5 $\times$ 10^-5 m
C)2.4 $\times$ 10^-5 m
D)4.7 $\times$ 10^-5 m
E)None of these is correct.

Question 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

Two slits of width a = 0.020 mm are separated by a distance d = 0.05 mm and illuminated by light of wavelength $\lambda$ = 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 42

Two slits of width a = 0.0016 mm are separated by a distance d = 0.04 mm and illuminated by light of wavelength $\lambda$ = 450 nm.The number of bright fringes seen in the central maximum is

A)8
B)16
C)25
D)37
E)49

Question 43

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 44

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 45

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 46

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 $\times$ 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 47

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 48

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 49

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 50

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 51

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.

Question 52

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 53

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 54

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 55

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 56

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 57

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 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

Question 59

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 60

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 $\times$ 10^-5 m
B)1.5 $\times$ 10^-5 m
C)3.0 $\times$ 10^-5 m
D)8.2 $\times$ 10^-5 m
E)3.8 $\times$ 10^-5 m

Question 61

A diffraction grating has 5000 lines per centimeter and is 1.5 centimeters wide.When radiation is incident upon the grating a second-order maximum is observed at an angle of 37º.The wavelength of this light is

A)400 nm
B)600 nm
C)900 nm
D)1200 nm
E)2400 nm

Question 62

For a given light source and collimator slit width,the spectral lines obtained using a prism are brighter than those using a diffraction grating because

A)the grating absorbs more light than the prism.
B)light is dispersed more by a prism than by a grating.
C)the prism forms a single spectrum and the grating forms multiple spectra.
D)light passes through the prism at minimum deviation.
E)light is dispersed more by a grating than by a prism.

Question 63

In accordance with the Rayleigh criterion,two points can be just resolved if the centers of their diffraction patterns are separated by

A)one wavelength.
B)twice the width of either central maximum.
C)one-half the width of either central maximum.
D)the width of the aperture.
E)the reciprocal of one wavelength.

Question 64

The type of electromagnetic radiation that is employed when crystals are used as diffraction gratings is

A)infrared
B)Xrays
C)visible
D)ultraviolet
E)microwaves

Question 65

Rayleigh's criterion is most closely associated with

A)diffraction
B)coherence
C)dispersion
D)polarization
E)reflection

Question 66

A diffraction grating has 2000 lines per centimeter and is 3.0 centimeters wide.When visible light is incident on the grating,a maximum is observed at an angle of 10º from the normal.The wavelength of the incident radiation is

A)435 nm
B)525 nm
C)600 nm
D)725 nm
E)870 nm

Question 67

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 590 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 2.00 m.The distance between the two dark fringes on each side of the central bright fringe is

A)0.295 cm
B)0.590 cm
C)1.18 cm
D)2.95 cm
E)5.90 cm

Question 68

Green light of wavelength 500 nm is incident normally on a diffraction grating that has 5300 lines/cm.The second-order image is diffracted at an angle from the normal of

A)10º
B)16º
C)32º
D)48º
E)57º

Question 69

For a given grating,it is observed that a third-order line (m = 3)with $\lambda$ = 465.3 nm overlaps a second-order line (has the same $\theta$ as a line with m = 2).The wavelength of the second-order line is

A)304 nm
B)698 nm
C)913 nm
D)152 nm
E)372 nm

Question 70

The size of the smallest things that can be seen with an optical microscope is limited by diffraction.Which of the following could help a microscopist see smaller things?

A)A more powerful microscope could be used.
B)The microscope could have a lens with a shorter focal length.
C)The microscope could have a lens with a longer focal length.
D)The diameter of the lens could be smaller.
E)Light with a shorter wavelength could be used.

Question 71

The headlights of an oncoming car are 1.2 m apart.What is the maximum distance from the car at which you can resolve the lights as two sources if the diameter of the pupil of your eye is 5.0 mm and the wavelength of the light is 555 nm?

A)8.9 km
B)22 km
C)4.4 km
D)5.4 km
E)13 km

Question 72

The pupil of the human eye has a diameter of about 5 mm.When the wavelength of light incident on the pupil is 500 nm,the smallest angular separation of two resolvable sources is approximately

A)1"
B)1'
C)1º
D)10º
E)1 radian

Question 73

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 600 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 1.50 m.The distance on the screen from the center of the central maximum to the first minimum is

A)0.675 cm
B)0.600 cm
C)0.300 cm
D)0.450 cm
E)0.225 cm

Question 74

For a grating with d = 3.5 $\lambda$ ,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

A)3.5
B)3
C)1
D)2
E)2.5

Question 75

Diffraction occurs when light passes

A)by a small particle.
B)through a small hole.
C)through a double slit.
D)by a sharp edge.
E)Diffraction occurs in all of these conditions.

Question 76

A monochromatic beam of light of wavelength 600 nm falls on a grating at normal incidence and produces a second-order image at an angle of 30º.The grating spacing must be

A)0.60 µm
B)2.4 µm
C)0.30 µm
D)1.4 µm
E)1.0 µm

Question 77

In demonstrating single-slit Fraunhofer diffraction,decreasing the wavelength of the light while keeping the slit width constant

A)does not affect the width of the central maximum.
B)increases the number of fringes within the central maximum.
C)decreases the number of fringes within the central maximum.
D)increases the width of the central maximum.
E)decreases the width of the central maximum

Question 78

The 200-in reflecting telescope at Mt.Palomar has an objective mirror with a focal length of 16.8 m.The effective aperture is the diameter of the 200-in mirror (200 in = 5.08 m).For light in the blue region (450 nm),what is the smallest angle between two stars that this telescope can ideally resolve? (In practice,the limit of resolution is due to atmospheric turbulence.)

A)1.1 $\times$ 10^-8 rad
B)1.1 $\times$ 10^-7 rad
C)7.3 $\times$ 10^-7 rad
D)1.1 $\times$ 10^-4 rad
E)8.9 $\times$ 10^-5 rad

Question 79

For a grating with d = 4.5 $\lambda$ ,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

A)4.5
B)3
C)1
D)2
E)4

Question 80

An antenna for receiving television signals from a satellite has a diameter of 3 m.The signals have a wavelength of 24 cm.If the diameter of the antenna is reduced to 50 cm,for what signal wavelengths does the antenna still have the same angular resolution?

A)4.0 cm
B)6.0 cm
C)8.0 cm
D)1.4 m
E)24 cm