Deck 35: Interference and Diffraction

Question 1

A monochromatic source produces light at a wavelength of 510 nm in air. The wave then passes through water that has an index of refraction of 1.32. The frequency of the wave in the water is

A) $7.76 \times 10 ^ { 14 }$ Hz.
B) $4.45 \times 10 ^ { 14 }$ Hz.
C) $5.88 \times 10 ^ { 14 }$ Hz.
D) $4.54 \times 10 ^ { 14 }$ Hz.

Answer 1

$5.88 \times 10 ^ { 14 }$ Hz.

Question 2

A monochromatic source produces light at a wavelength of 510 nm in air. The wave then passes through water that has an index of refraction of 1.32. The velocity of propagation of the wave in the water is

A) $2.27 \times 10 ^ { 8 }$ m/s.
B) $3.96 \times 10 ^ { 8 }$ m/s.
C) $2.96 \times 10 ^ { 8 }$ m/s.
D) $$3.00 \times 10 ^ { 8 }$$ m/s.

Answer 2

$2.27 \times 10 ^ { 8 }$ m/s.

Question 3

A monochromatic source produces light at a wavelength of 510 nm in air. The wave then passes through water that has an index of refraction of 1.32. The wavelength of the wave in the water is

A) 673 nm.
B) $386$ nm.
C) 510 nm.
D) 623 nm.

Answer 3

$386$ nm.

Question 4

Red light having a wavelength of 690 nm (in air) is vertically incident on a thin film of oil that has an index of refraction of 1.19. The film of oil floats above water (having an index of refraction of 1.30). No red light is reflected. The minimum (nonzero) thickness of the film of oil is

A) 290 nm.
B) 345 nm.
C) 580 nm.
D) 145 nm.

Question 5

Red light having a wavelength of 690 nm (in air) is vertically incident on a thin film of oil that has an index of refraction of 1.19. The film of oil floats above water (having an index of refraction of 1.30). The red light is brightly reflected. The minimum (nonzero) thickness of the film of oil is

A) 290 nm.
B) 345 nm.
C) 580 nm.
D) 145 nm.

Question 6

Green light having wavelength of 550 nm (in air) is vertically incident on a thin film of water that has an index of refraction of 1.30. The film of water rests above a plastic pane (having an index of refraction of 1.22). The green light is brightly reflected. The minimum (nonzero) thickness of the film of water is

A) 212 nm.
B) 450 nm.
C) 423 nm.
D) 108 nm.

Question 7

Green light having a wavelength of 550 nm (in air) is vertically incident on a thin film of water that has an index of refraction of 1.30. The film of water rests above a plastic pane (having an index of refraction of 1.22). No green light is reflected. The minimum (nonzero) thickness of the film of water is

A) 212 nm.
B) 450 nm.
C) 423 nm.
D) 108 nm.

Question 8

Consider a Young's double-slit experiment. The slits are separated by 1.2 mm, and the monochromatic light has a wavelength of 600 nm. The angular position of the first-order bright (maxima) fringe is

A) 0.054º.
B) 0.018º.
C) 0.029º.
D) 0.035º.

Question 9

Consider a Young's double-slit experiment. the slits are separated by 1.2 mm, and the monochromatic light has a wavelength of 600 nm. The angular position of the first-order dark (minima) fringe is

A) 0.044º.
B) 0.014º.
C) 0.022º.
D) 0.036º.

Question 10

In a Young's double-slit experiment, the time-averaged value of $\cos ^ { 2 } \left( \omega t - 2 \pi r _ { 0 } / \lambda \right)$ , where $r _ { 0 }$ is the distance from the center of the slits to the point of interest, and $\lambda$ is the wavelength of light, is

A) 0
B) 1/2.
C) $r _ { 0 } / \lambda .$
D) $1 / \sqrt { 2 }$

Question 11

In a Young's double-slit experiment, when $( \pi d / \lambda ) \sin \theta$ is an odd half-multiple of $\pi ( \pi / 2,3 \pi / 2,5 \pi / 2 )$ the intensity at the viewing screen

A) is a maximum.
B) is a minimum.
C) is halfway between the maximum and minimum.
D) cannot be determined we need $d , \lambda , \text { and } \theta$

Question 12

In a Young's double-slit experiment, when $( \pi d / \lambda ) \sin \theta$ is a multiple of ( $\pi ( \pi , 2 \pi , 3 \pi )$ ), the intensity at the viewing screen

A) is a maximum.
B) is a minimum.
C) is halfway between the maximum and minimum.
D) cannot be determined (we need $d , \lambda , \text { and } \theta$ )

Question 13

The intensity $\text { I }$ of an electromagnetic wave (having electric field $E$ ) is proportional to

A) $E$
B) $\sqrt { E }$
C) $E ^ { 2 }$
D) $E ^ { 4 }$

Question 14

An electric field phasor makes an angle of $\omega t$ relative to the x axis. The instantaneous value of the electric field is given by the

A) projection of the phasor along the y axis.
B) magnitude of the phasor.
C) projection of the phasor along the x axis.
D) direction of the phasor.

Question 15

An electric field phasor makes an angle of $\omega t$ relative to the x axis. As time increases the phasor rotates

A) about the origin in a counterclockwise manner.
B) around the y axis.
C) about the origin in a clockwise manner.
D) in an undetermined direction.

Question 16

An electric field phasor of length 2300 V/m makes an angle of $\omega t = 30 ^ { \circ }$ relative to the x axis. What is the instantaneous value of the electric field?

A) 2000 V/m
B) 1200 V/m
C) 1300 V/m
D) 2300 V/m

Question 17

"Every point in space can be regarded as a wave source" is known as

A) the Doppler effect.
B) Young's interference phenomena.
C) the Huygens-Fresnel principle.
D) Gauss' law.

Question 18

The first angular minima location for a single-slit diffraction having slit width of $1 \mu \mathrm { m }$ and wavelength of 500 nm is

A) 10º.
B) 45º.
C) 20º.
D) 30º.

Question 19

The second angular minima location for a single-slit diffraction having slit width of $1.5 \mu \mathrm { m }$ and wavelength of 500 nm is

A) 13º.
B) 42º.
C) 25º.
D) 36º.

Question 20

The diffraction pattern produced by a single rectangular slit is known as

A) an Airy diffraction.
B) a Fraunhofer diffraction.
C) a Huygens diffraction.
D) a Fresnel diffraction.

Question 21

The width of the central maximum diffraction pattern produced by a single slit will increase when

A) the slit width decreases.
B) the slit width increases.
C) the wavelength decreases.
D) None of the previous answers is correct.

Question 22

The limiting angular separation of two points such that they can be resolved is known as

A) Rayleigh's criterion.
B) Kepler's law.
C) Doppler's law.
D) Galileo's principle.

Question 23

Find the critical angle for two objects 1 meter apart when viewed using 500-nm light (assume a rectangular aperture):

A) $5 \times 10 ^ { - 7 }$ radians
B) $6 \times 10 ^ { - 5 }$ radians
C) $9 \times 10 ^ { - 6 }$ radians
D) $7 \times 10 ^ { - 6 }$ radians

Question 24

Find the critical angle for two objects 1 meter apart when viewed using 500-nm light (assume a circular aperture):

A) $$6 \times 10 ^ { - 7 }$$ radians
B) $4 \times 10 ^ { - 5 }$ radians
C) $8 \times 10 ^ { - 6 }$ radians
D) $5 \times 10 ^ { - 6 }$ radians

Question 25

The critical angle for two objects 1 meter apart is $10 ^ { - 6 }$ radians. Estimate the wavelength of the light:

A) 550 nm
B) 630 nm
C) 820 nm
D) 710 nm

Question 26

Direct observation of a standing wave pattern associated with light is difficult. The most relevant reason is that

A) the eye is insensitive to fluctuations in intensity that occur at those frequencies.
B) the eye cannot resolve a pattern with that spacing.
C) there is no convenient means of setting up the conditions for standing waves.
D) Hold it! In principle, light is not capable of producing standing waves.

Question 27

All of the following considerations are important in explaining the observed interference patterns produced by light reflection from a thin film except

A) the superposition of incident light with reflected light.
B) the superposition of reflections coming from separate points on the reflecting surface.
C) the time average of the intensity of the light at places that are not nodes.
D) the relative magnitudes of the E-fields contributing to the resultant nodal points.

Question 28

When light reflects from a thin film, the distance between the fringes depends on all of the following except

A) the change in film thickness.
B) the light frequency.
C) the index of refraction of the film.
D) Hold it! There are no exceptions.

Question 29

When light reflects from a thin film, whether or not a phase shift occurs at one or both of the reflecting surfaces, the single characteristic of the fringes that is affected by this potential change is

A) their separation.
B) their position.
C) their sense (dark followed by bright, or vice versa).
D) None of the previous responses is valid.

Question 30

When light reflects from a thin film, the distance between adjacent bright regions of the fringes depends on the path difference being equal to the wavelength of the light times

A) 1/4.
B) 1/2.
C) 1.
D) 2.

Question 31

When light reflects from a thin film, the distance between adjacent bright regions of the fringes depends on the film thickness being equal to the wavelength of the light times

A) 1/4.
B) 1/2.
C) 1.
D) 2.

Question 32

There is invariably a phase shift when light reflects from a surface such that the index of refraction in which the wave is propagating is

A) > 1.
B) > the index of the material beyond the reflecting surface.
C) = the index of the material beyond the reflecting surface.
D) < the index of the material beyond the reflecting surface.

Question 33

The minimum film thickness for which a reflection maximum occurs is the same in all of the following situations except

A) when the film is surrounded by a material of larger index of refraction.
B) when the film is surrounded by a material of smaller index of refraction.
C) when the film is bordered by a material of larger index of refraction on one side and a material of smaller index of refraction on the other side.
D) Hold it! There are no exceptions.

Question 34

When reflection fringes associated with a thin film are not uniformly spaced, the reason could be nonuniformities in

A) the film thickness.
B) the film index of refraction.
C) Both of the first two responses are valid.
D) Neither of the first two responses is valid.

Question 35

If two sources emit waves that are of the same frequencies and are in phase, the interference fringes produced will appear to the human eye to be

A) stationary in space.
B) stationary in time.
C) Both of the first two responses are valid.
D) Neither of the first two responses is valid.

Question 36

If two sources emit waves that are not of the same frequencies and do not remain in phase, the interference fringes produced will actually be

A) moving in space.
B) moving in time.
C) Both of the first two responses are valid.
D) Hold it! Interference cannot be produced.

Question 37

When two slits are replaced with three slits (with the same slit-to-slit spacing), all of the following changes occur in the interference fringe pattern except

A) the angular separation between principal maxima and the adjacent points of minima is reduced.
B) it is no longer dark at the points where the two-slit minima were located.
C) the principal maxima are more closely spaced.
D) the principal maxima are brighter.

Question 38

White light shining onto a grating or onto a prism is "separated" into different colors. By comparison,

A) in the grating and in the prism, red light is "bent" more than blue light.
B) in the grating and in the prism, red light is "bent" less than blue light.
C) in the grating, red light is "bent" less than blue light; in the prism, blue light is "bent" less than red light.
D) in the grating, red light is "bent" more than blue light; in the prism, blue light is "bent" more than red light.

Question 39

The explanation for the correct response to the previous question involves the two facts that red light has a wavelength that is

A) longer than that of blue light, and it travels slower in glass than blue light.
B) longer than that of blue light, and it travels faster in glass than blue light.
C) shorter than that of blue light, and it travels faster in glass than blue light.
D) shorter than that of blue light, and it travels slower in glass than blue light.

Question 40

White light shining onto a grating or onto a prism is "separated" into different colors. Contrasts include all of the following except

A) in the grating, the whole separation sequence may be repeated at larger angles.
B) in the grating, the separation does not involve refraction.
C) in the grating, there is a central region where the colors are not separated.
D) Hold it! There are no exceptions.

Question 41

The resolving power for a grating increases with an increase in

A) the number of slits.
B) the separation of slits.
C) the wavelength of light.
D) none of the above.

Question 42

The width of a principal maximum for a grating decreases with an increase in each of the following except

A) the number of slits.
B) the separation of slits.
C) the wavelength of light.
D) Hold it! There are no exceptions.

Question 43

The angular separation between successive principal maxima for a grating decreases with increasing

A) number of slits.
B) separation of slits.
C) wavelength of light.
D) Hold it! None of the previous responses is valid.

Question 44

In comparing two gratings, the one with the greater resolving power must invariably provide for

A) a larger angular separation of adjacent maxima for the two wavelengths.
B) a smaller angular spread from the maxima of each wavelength to the adjacent minima.
C) a larger ratio of angular separation of the two wavelengths to angular spread from maxima to minima for each.
D) a smaller ratio of angular separation of the two wavelengths to angular spread from maxima to minima for each.

Question 45

In designing a grating, the way to achieve a larger angular separation of adjacent maxima for two approximately equal wavelengths is to

A) make the slits closer together.
B) increase the number of slits.
C) look at larger-order maxima.
D) Hold it! More than one response is valid.

Question 46

In designing a grating, the way to achieve a smaller angular spread from the maxima of each wavelength to the corresponding minima for two approximately equal wavelengths is to

A) make the slits closer together.
B) increase the number of slits.
C) look at larger-order maxima.
D) Hold it! More than one response is valid.

Question 47

When two pieces of glass are pressed together in air and illuminated with coherent light, the place where they are in contact will look

A) dark.
B) bright.
C) Hold it! Its appearance will oscillate between dark and bright.
D) Hold it! Though the appearance will be steady in time, more information is needed to answer this question unambiguously.

Question 48

When two pieces of glass are pressed together in air and illuminated with coherent light, the place where they are in contact will exhibit an appearance correctly described in one of the responses to the preceding question. The reason behind the correct answer is that

A) the actual physical path difference between waves striking the two surfaces in contact is very close to zero.
B) the phase difference between waves reflected from the two surfaces is 180º.
C) Both of the first two responses are necessary to obtain the correct answer.
D) Though both of the first two responses state facts correctly, neither is relevant in explaining the correct answer to the previous question.

Question 49

Two very flat pieces of glass touch at one edge and are held apart by a small wire at the other edge. Illumination from above by coherent light of wavelength 5000 angstroms results in 20 dark fringes between the touching surfaces and where the wire is located. The approximate diameter of the wire is

A) 200,000 angstroms.
B) 100,000 angstroms.
C) 50,000 angstroms.
D) 25,000 angstroms.

Question 50

The angular separation between principal maxima for a grating consisting of 10,000 slits is 30º. The approximate angular width of the principal maxima is

A) .003º.
B) .3º.
C) 30º.
D) Hold it! The angle is much greater than 360º.