Deck 24: Physical Optics: The Wave Nature of Light

Question 1

Why would it be impossible to obtain interference fringes in a double-slit experiment if the separation of the slits is less than the wavelength of the light used?

Answer 1

In no direction could a path difference as large as one wavelength be obtained, and this is needed if a bright fringe, in addition to the central fringe, is to be observed.

Question 2

Why does light seem to go straight through an open doorway whereas sound seems to spread out when it goes through the same doorway?

Answer 2

It has to do with the relative sizes of their wavelengths. The wavelength of light is << opening size so very small diffraction; sound wavelengths are >> opening so diffraction is significant.

Question 3

Discuss a similarity and a difference between the spectrum formed by a diffraction grating (a large number of slits) and that formed by just a double slit.

Answer 3

The maxima of both satisfy d sin(θ) = nλ, but the fringes formed by the grating are much sharper (narrow).

Question 4

How do interference and diffraction differ? How are they similar?

Question 5

Discuss what you see viewing a distant street light through a thin curtain (at night).

Question 6

If two light waves are coherent, which of the following is NOT necessary?

A) They must have the same velocity.
B) They must have the same wavelength.
C) They must have the same amplitude.
D) They must have the same frequency.
E) They must have a constant phase difference at every point in space.

Question 7

The experiments of what person first clearly demonstrated the wave nature of light?

A) Maxwell
B) Young
C) Newton
D) Einstein
E) Galileo

Question 8

Monochromatic light from a distant source is incident on two parallel narrow slits. After passing through the slits the light strikes a screen, as shown in Figure 24-1.

What will be the nature of the pattern of light observed on the screen?

A) A rainbow of colored lines will be seen spreading out on either side of point O.
B) The screen will be uniformly illuminated except for two dark bands, one in line with each slit.
C) There will be two bright bands of light, one in line with each slit.
D) There will be a series of alternating light and dark bands.
E) The screen will be most brightly illuminated at point O, with the intensity decreasing slowly and uniformly as you move outward from point O.

Question 9

Constructive interference of two coherent waves will occur if the path difference is

A) 1/4 $\lambda$ .
B) 6/4 $\lambda$ .
C) 6/2 $\lambda$ .
D) 3/4 $\lambda$ .
E) 3/2 $\lambda$ .

Question 10

At the first maxima on either side of the central bright spot in a double-slit experiment, light from each opening arrives

A) in phase.
B) 45° out of phase.
C) 90° out of phase.
D) 180° out of phase.
E) -45° out of phase.

Question 11

Two beams of coherent light travel different paths arriving at point P. If the maximum constructive interference is to occur at point P, the two beams must

A) arrive 180° out of phase.
B) arrive 90° out of phase.
C) travel paths that differ by an odd number of half-wavelengths.
D) travel paths that differ by a whole number of wavelengths.

Question 12

The path difference for destructive interference is m $\lambda$ /2 where

A) m = 0, 1, 2, 3, ...
B) m = 2, 4, 6 , 8, ...
C) m = 0, 2, 4, 6, ...
D) m = 1, 3, 5, 7, ...
E) m = 1, 2, 3, 4, ...

Question 13

In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1 cm. What happens to the distance between adjacent maxima when the slit separation is cut in half?

A) It increases to 2 cm.
B) It decreases to 0.5 cm.
C) It increases to 4 cm.
D) It decreases to 0.25 cm.

Question 14

At the second maxima on either side of the central bright spot in a double-slit experiment, light from

A) one opening travels two wavelengths of light farther than light from the other opening.
B) each opening travels the same distance.
C) one opening travels twice as far as light from the other opening.
D) one opening travels one wavelength of light farther than light from the other opening.

Question 15

The separation between adjacent maxima in a double-slit interference pattern using monochromatic light is

A) greatest for blue light.
B) greatest for green light.
C) greatest for red light.
D) the same for all colors of light.

Question 16

The colors on an oil slick are caused by reflection and

A) refraction.
B) polarization.
C) interference.
D) diffraction.

Question 17

The concentric fringes, formed when a curved lens is placed on an optical flat, are called

A) Galileo circles.
B) Faraday's circles.
C) Newton's rings.
D) Young's rings.
E) Maxwell circles.

Question 18

After a rain, one sometimes sees brightly colored oil slicks on the road. These are due to

A) polarization effects.
B) selective absorption of different wavelengths by oil.
C) diffraction effects.
D) interference effects.
E) birefringence.

Question 19

Liquid Crystal Displays (LCDs) depend upon which of the following for their operation?

A) coherence
B) thin film interference
C) diffraction
D) dichroism
E) polarization

Question 20

The polarization of sunlight is greatest at

A) sunrise.
B) sunset.
C) midday.
D) both sunrise and sunset.

Question 21

We have seen that two monochromatic light waves can interfere constructively or destructively, depending on their phase difference. One consequence of this phenomena is

A) the formation of an image by a converging lens, such as the lens in your eye.
B) a rainbow.
C) the way in which polaroid sunglasses work.
D) the appearance of a mirage in the desert.
E) the colors you see when white light is reflected from a soap bubble.

Question 22

In terms of the wavelength of light in soapy water, what is the minimum thickness of soap film that will reflect a given wavelength of light?

A) one-half wavelength
B) two wavelengths
C) one wavelength
D) one-fourth wavelength
E) there is no minimum thickness

Question 23

A soap film is being viewed in white light. As the film becomes very much thinner than the wavelength of blue light, the film

A) appears black because it reflects no visible light.
B) appears white because it reflects all wavelengths of visible light.
C) appears red since all other colors are transmitted.
D) appears blue since all other colors are transmitted.

Question 24

A convex lens is placed on a flat glass plate and illuminated from above with monochromatic red light. When viewed from above, concentric bands of red and dark are observed. What does one observe at the exact center of the lens where the lens and the glass plate are in direct contact?

A) a bright red spot
B) a dark spot
C) a bright spot that is some color other than red
D) a rainbow of color

Question 25

Sunlight reflected from the surface of a lake

A) is unpolarized.
B) has undergone refraction by the surface of the lake.
C) is totally polarized.
D) tends to be polarized with its electric field vector parallel to the surface of the lake.
E) tends to be polarized with its electric field vector perpendicular to the surface of the lake.

Question 26

The condition for interference maxima for a diffraction grating is identical to that for

A) a narrowing single slit.
B) a wide single slit.
C) a double slit.
D) a thin film.

Question 27

Single-slit diffraction is characterized by

A) narrowing of diffraction pattern as slit width is reduced.
B) a distance between fringes which is independent of wavelength.
C) rapid decrease in intensity of higher order fringes.
D) decreasing angular separation of fringes as the order (m) increases.

Question 28

In single-slit diffraction

A) the central maximum is about as wide as the other maxima.
B) the slit width must be less than one wavelength for a diffraction pattern to be apparent.
C) the central maximum is about twice as wide as the other maxima.
D) the intensities of successive maxima are roughly the same, falling off only gradually as one goes away from the central maximum.
E) the central maximum is much narrower than the other maxima.

Question 29

Consider two diffraction gratings; one has 4000 lines per cm and the other one has 6000 lines per cm.

A) Both gratings produce the same dispersion, but the orders are sharper for the 6000-line grating.
B) The 4000-line grating produces the greater dispersion.
C) Both gratings produce the same dispersion, but the orders are sharper for the 4000-line grating.
D) The 6000-line grating produces the greater dispersion.

Question 30

Consider two diffraction gratings with the same slit separation, the only difference being that one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic light

A) both gratings produce the same separation between orders, but the orders are better defined with the 4-slit grating.
B) the grating with 4 slits produces the greater separation between orders.
C) the grating with 3 slits produces the greater separation between orders.
D) both gratings produce the same separation between orders.

Question 31

The condition 2d sin( $\theta$ ) = n $\lambda$ for X-ray diffraction maxima is attributed to

A) Land.
B) Rayleigh.
C) Bragg.
D) Young.
E) Brewster.

Question 32

Another name for the POLARIZING ANGLE is the

A) Brewster angle.
B) Moles angle.
C) Land angle.
D) refracted angle.

Question 33

A material which has the ability to rotate the direction of polarization of linearly polarized light is said to be

A) circularly polarized.
B) dichroic.
C) optically active.
D) diffraction limited.
E) birefringent.

Question 34

Two emerging beams of light produced by a birefringent crystal

A) will produce an interference pattern when recombined.
B) are polarized in mutually perpendicular directions.
C) are polarized in the same direction.
D) are at different frequencies.
E) are at 90° with respect to one another.

Question 35

Suppose that you take the lenses out of a pair of polarized sunglasses and place one on top of the other. Rotate one lens 90° with respect to the normal position of the other lens. Early in the morning, look directly overhead at the sunlight coming down. What would you see?

A) You would see light with intensity reduced to about 50% of what it would be with one lens.
B) You would see some light, and the brightness would be a function of how the lenses were oriented with respect to the incoming light.
C) You would see some light, and the intensity would be greater than if you looked through only one lens.
D) The lenses would look completely dark, since they would transmit no light.
E) You would see some light, and the intensity would be the same as if you had looked through only one lens.

Question 36

If sunlight of color B is scattered through an angle 16 times greater than sunlight of color A, then the wavelength of color B is

A) twice that of color A.
B) 1/4 that of color A.
C) 1/16 that of color A.
D) 1/2 that of color A.
E) 16 times that of color A.

Question 37

The sky appears "blue" because of

A) birefringence.
B) Rayleigh scattering.
C) Brewster's polarization.
D) dichroism.
E) Bragg's Law.

Question 38

On a clear day, the sky appears to be more blue toward the zenith (overhead) than it does toward the horizon. This occurs because

A) the atmosphere is denser higher up than it is at the earth's surface.
B) the atmosphere is more reddish over the ocean.
C) the temperature of the upper atmosphere is higher than it is at the earth's surface.
D) the sunlight travels over a longer path at the horizon, resulting in more absorption.

Question 39

For what slit separation will no 1st order double-slit-fringe appear for 550. nm light?

Question 40

A lens is coated with material of index of refraction 1.38. What thickness of coating should be used to give maximum transmission at a wavelength of

Question 41

A glass plate 2.5 cm long is separated from another glass plate by a strand of someone's hair (diameter 0.010 mm). How far apart are the adjacent interference bands when viewed with light of wavelength 600 nm?

Question 42

A beam of light passes through a polarizer and then an analyzer. In this process, the intensity of the light transmitted is reduced to 10% of the intensity incident on the analyzer. What is the angle between the axes of the polarizer and the analyzer?

Question 43

Light precedes through three polarizing sheets. Unpolarized light enters the 1st sheet and the resultant vertically polarized beam continues through the 2nd and 3rd. The 2nd sheet has its transmission axis at 50.° with respect to the 1st, and the 3rd is at 70.° with respect to the 1st.
(a) What percent of the original intensity emerges from filter #1?
(b) What percent of the original intensity emerges from filter #2?
(c) What percent of the original intensity emerges from filter #3?
(d) If filter 2 has its transmission axis changed to 30.°, what % intensity now emerges from the 3rd filter?

Question 44

Consider 550. nm light passing through 2 narrow slits 2.10 micro-meters apart. The 1st and 2nd order fringes are 1.00 mm apart on a distant screen. How far apart are the 2nd and 3rd order fringes?

A) 0.750 mm
B) 0.500 mm
C) 1.74 mm
D) 1.00 mm
E) 1.35 mm

Question 45

Light of wavelength $\lambda$ = 540 nm passes through a pair of slits with separation 3.4 × 10^-5 m. What is the angle corresponding to the second bright fringe?

A) 1.5°
B) 4.3°
C) 5.0°
D) 3.7°
E) 1.8°

Question 46

Light in a frozen block of ice reflects off the ice-air interface and undergoes a phase shift of

A) 0°.
B) 180°.
C) 270°.
D) 90°.

Question 47

Light which reflects off a pond of water undergoes a phase shift of

A) 90°.
B) 0°.
C) 180°.
D) 270°.
E) 45°.

Question 48

Consider an oil film (n = 1.50) on water (n = 1.33) and 600. nm incident light. The minimum film thickness for constructive interference is

A) 200. nm.
B) 113. nm.
C) 150. nm.
D) 100. nm.

Question 49

In a single-slit diffraction experiment, a beam of monochromatic light passes through a slit of width 11.0 $\mu$ m. If the first order dark fringe of the resulting diffraction pattern is at an angle of 4.61°, what is the wavelength of light?

A) 402 nm
B) 602 nm
C) 201 nm
D) 301 nm
E) 884 nm

Question 50

How many orders are in the spectra formed by a grating with 3000. lines/cm illuminated by red light of wavelength 600. nm?

A) 0
B) 5
C) 1
D) 4
E) 3

Question 51

What is the slit spacing of a diffraction necessary for a 600 nm light to have a first order principal maximum at 25.0°?

A) 3.12 $\mu$ m
B) 4.12 $\mu$ m
C) 5.44 $\mu$ m
D) 1.42 $\mu$ m
E) 2.01 $\mu$ m

Question 52

At what angle, with the surface, must light strike glass (refractive index 1.6) in order to completely polarize the reflected ray?

A) 56.°
B) 32°
C) 11.°
D) 86.°
E) 34.°

Question 53

A ray of light traveling in water (n = 1.33) hits a glass surface (n = 1.50). At what angle, with the surface, must the incident ray be in order that the polarization of the reflected ray is the greatest?

A) 36.9°
B) 33.7°
C) 41.6°
D) 48.4°
E) 53.1°

Question 54

An ideal polarizer is placed in a beam of unpolarized light and the intensity of the transmitted light is 1.000. A second ideal polarizer is placed in the beam with its referred direction rotated 40° to that of the first polarizer. What is the intensity of the beam after it has passed through both polarizers?

A) 0.6431
B) 0.5868
C) 0.5000
D) 0.4131
E) 0.7661

Question 55

A polarizer (with its preferred direction rotated 30° to the vertical) is placed in a beam of unpolarized light of intensity 1. After passing through the polarizer, the beam's intensity is

A) 0.7501.
B) 0.5001.
C) 0.2501.
D) 0.8661.
E) 0.5000.

Question 56

What is the Brewster's angle for light traveling in vacuum and reflecting off a piece of glass of index of refraction 1.52?

A) 48.9°
B) 56.7°
C) 41.1°
D) 33.3°
E) 48.1°

Question 57

Rayleigh scattering would have 400. nm light be scattered how many times as much as 800. nm light?

A) 8
B) 16
C) 2
D) 4
E) 32