Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Two radio antennas are 120 m apart on a north-south line. The two antennas radiate in phase at
a frequency of 3.4 MHz. All radio measurements are made far from the antennas. The smallest
angle, reckoned east of north from the antennas, at which constructive interference of two radio
waves occurs, is closest to:
A) 47°
B) 34°
C) 38°
D) 30°
E) 43°
1)
2) Two radio antennas are 100 m apart on a north-south line. The two antennas radiate in phase at
a frequency of 4.9 MHz. All radio measurements are made far from the antennas. The smallest
angle, reckoned north of east from the antennas, at which destructive interference of the two
radio waves occurs, is closest to:
A) 22°
B) 13°
C) 27°
D) 8.9°
E) 18°
2)
3) Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at
a frequency of 4.7 MHz. All radio measurements are made far from the antennas. Point A is due
east of the antennas and point B is 30° north of east from the antennas. Both points A and B are at
the same large distance from the antennas. The ratio of the intensity of the radio signal at B to
that at A is closest to:
A) 1.0
B) 1.5
C) 3.0
D) 0.50
E) 2.0
3)
4) Two radio antennas are 10 km apart on a north-south axis on a seacoast. The antennas broadcast
identical AM radio signals, in phase, at a frequency of 8.20 MHz. A steamship, 200 km offshore,
travels due north at a speed of 15 km/hr and passes east of the antennas. A radio on board the
ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a
maximum at a given instant. The time interval until the next occurrence of maximum reception
is closest to:
A) 5.1 min
B) 2.2 min
C) 3.7 min
D) 4.4 min
E) 2.9 min
4)
5) Two radio antennas are 10 km apart on a north-south axis on a seacoast. The antennas broadcast
identical AM radio signals, in phase, at a frequency of 6.80 MHz. A steamship, 200 km offshore,
travels due north at a speed of 15 km/hr and passes east of the antennas. A radio on board the
ship is tuned to the broadcast frequency. Four minutes after a radio signal of maximum intensity
is received, the ratio of the intensity of the signal received to the maximum intensity is closest to:
A) 0.25
B) 0.50
C) 0.83
D) 0.93
E) 0.88
5)
1
Figure 35.1a
6) An FM radio transmitter, operating at a frequency of 120 MHz, is atop a 100-m tower. An
airplane is in flight over the ocean at an altitude of 2000 m. Radio waves reach the airplane
directly from the transmitter and by reflection from the surface of the ocean. When the airplane
is 86 km from the tower, the pilot observes that radio reception has faded due to destructive
interference of the waves in the two paths. Assume the wave reflected from the ocean surface
has undergone a half-wave phase shift. In Fig. 35.1a, the waves of the reflected path arrive at the
airplane delayed, with respect to the direct path. The time interval of this delay, in ns, is closest
to:
A) 20
B) 18
C) 22
D) 14
E) 16
6)
Figure 35.1b
7) An FM radio transmitter, operating at a frequency of 120 MHz, is atop a 100 m tower. An
airplane is in flight over the ocean at an altitude of 2000 m. Radio waves reach the airplane
directly from the transmitter and by reflection from the surface of the ocean. When the airplane
is 89 km from the tower, the pilot observes that radio reception has faded due to destructive
interference of the waves in the two paths. Assume the wave reflected from the ocean surface
has undergone a half-wave phase shift. In Fig. 35.1b, the ratio of the difference in the lengths of
the two radio paths to the wavelength is closest to:
A) 2.0
B) 1.9
C) 2.1
D) 2.2
E) 1.8
2
7)
Figure 35.2a
8) A 610-nm thick film, of index n 1 = 1.40, is on the surface of a glass plate, of index n 2 = 1.55. A
ray of monochromatic light, of 500-nm wavelength, is incident normally upon the air-film
interface, and undergoes reflections and transmissions. Consider points A, B, C, and D as being
at a negligible distance from their nearest interfaces, respectively. In Fig. 35.2a, the phase
difference in the wave at B, with respect to the wave at A, is closest to:
A) 8.6 rad
B) 8.7 rad
C) 11 rad
D) 9.6 rad
E) 12 rad
8)
Figure 35.2b
9) A 250-nm thick film, of index n 1 = 1.40, is on the surface of a glass plate, of index n 2 = 1.55. A
ray of monochromatic light, of 500-nm wavelength, is incident normally upon the air-film
interface, and undergoes reflections and transmissions. Consider points A, B, C, and D as being
at a negligible distance from their nearest interfaces, respectively. In Fig. 35.2b, the phase
difference in the wave at C, with respect to the wave at A, is closest to:
A) 3.3 rad
B) 4.4 rad
C) 5.5 rad
D) 1.3 rad
E) 2.3 rad
3
9)
Figure 35.2c
10) A 880-nm thick film, of index n 1 = 1.40, is on the surface of a glass plate, of index n 2 = 1.55. A
ray of monochromatic light, of 500-nm wavelength, is incident normally upon the air-film
interface, and undergoes reflections and transmissions. Consider points A, B, C, and D as being
at a negligible distance from their nearest interfaces, respectively. In Fig. 35.2c, the phase
difference in the wave at D, with respect to the wave at A, is closest to:
A) 33 rad
B) 28 rad
C) 31 rad
D) 29 rad
E) 30 rad
10)
11) Light of wavelength 425.0 nm in air falls at normal incidence on an oil film that is 850.0 nm thick.
The oil is floating on a water layer 1500 nm thick. The refractive index of water is 1.33, and that
of the oil is 1.40. The number of wavelengths of light that fit in the oil film is closest to:
A) 2.80
B) 2.66
C) 3.53
D) 4.69
E) 2.00
11)
12) Light of wavelength 425.0 nm in air falls at normal incidence on an oil film that is 850.0 nm thick.
The oil is floating on a water layer 1500 nm thick. The refractive index of water is 1.33, and that
of the oil is 1.40. You want to add oil so that light reflected off of the top of the oil film will be
canceled. The minimum distance that you should increase the oil film is closest to:
A) 121 nm
B) 106 nm
C) 152 nm
D) 75.9 nm
E) 60.7 nm
12)
13) At most, how many bright fringes can be formed on one side of the central bright fringe (not
counting the central bright fringe) when light of 625 nm falls on a double slit whose spacing is
2.81 × 10-6 m?
13)
A) 2
B) 3
C) 4
D) 5
E) 6
Situation 35.1
A 360-nm thick oil film floats on the surface of the water. The indices of refraction of the oil and the water are 1.50 and
1.33, respectively. The surface of the oil is illuminated from above at normal incidence with white light.
14) In Situation 35.1, the two wavelengths of light in the 400-nm to 800-nm wavelength band that
are most strongly reflected, in nm, are closest to:
A) 430 and 720
B) 450 and 740
C) 410 and 700
D) 470 and 760
E) 490 and 780
4
14)
15) In Situation 35.1, the wavelength of light in the 400-nm to 800-nm wavelength band that is most
weakly reflected, in nm, is closest to:
A) 520
B) 580
C) 600
D) 540
E) 560
15)
Situation 35.2
A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. Light waves arrive at the
two slits in phase. A fringe pattern is observed on a screen 4.8 m from the slits.
16) In Situation 35.2, there are 5.0 bright fringes/cm on the screen. The wavelength of the
monochromatic light is closest to:
A) 650 nm
B) 750 nm
C) 700 nm
D) 600 nm
E) 550 nm
16)
17) In Situation 35.2, monochromatic light of 450-nm wavelength is used. The angular separation
between adjacent dark fringes on the screen, measured at the slits, in m rad, is closest to:
A) 0.15
B) 0.20
C) 0.36
D) 0.30
E) 0.25
17)
Situation 35.3
Two optically flat glass plates, 16 cm long, are in contact at one end and separated by 0.020 mm at the other end. The
space between the plates is occupied by oil with index of refraction 1.45. The index of the glass plates is 1.55. The plates
are illuminated at normal incidence with monochromatic light, and fringes are observed.
18) In Situation 35.3, the monochromatic light has a wavelength of 580 nm. The number of bright
fringes that are visible is closest to:
A) 80
B) 60
C) 90
D) 70
E) 100
18)
19) In Situation 35.3, the spacing of the dark fringes is 2.0 mm. The wavelength of the
monochromatic light, in nm, is closest to:
A) 475
B) 675
C) 525
D) 725
19)
E) 425
Figure 35.3
Coherent monochromatic light of wavelength 632.8 nm passes through a pair of thin parallel slits. Fig. 35.3 shows the
central portion of the pattern of bright fringes viewed on a screen 1.40 m beyond the slits.
20) For the two slits in Fig. 35.3, the distance between them is closest to:
A) 0.0703 mm
B) 0.281 mm
C) 0.562 mm
D) 0.633 mm
E) 0.141 mm
5
20)
21) For the two slits in Fig. 35.3, suppose we decrease the wavelength of the light by half, making it
316.4 nm. Assume that we can still detect the bright spots with instruments, even though we
cannot see them. The width of the nine-spot pattern shown in Fig.35.3 would now be closest to:
A) 0.630 cm
B) 1.78 cm
C) 5.04 cm
D) 10.1 cm
E) 1.26 cm
21)
Situation 35.4
The curved surface of a plano-convex glass lens is placed on an optically flat glass plate. The radius of curvature of the
convex surface is 40 cm. The plane surface of the lens is illuminated at normal incidence with monochromatic light and
Newton's rings are observed by reflection. Do not consider the center spot as a ring.
22) In Situation 35.4, the light has a wavelength of 720 nm. The radius of the third bright ring, in
mm, is closest to:
A) 0.85
B) 0.76
C) 0.66
D) 0.93
E) 1.00
22)
23) In Situation 35.4, the radius of the third dark ring is 0.80 mm. The wavelength of the light, in nm,
is closest to:
A) 650
B) 490
C) 580
D) 530
E) 620
23)
Situation 35.5
The mirrors of a Michelson interferometer are 5.0 cm wide. Monochromatic light of 450-nm wavelength is used and 12.0
fringes are observed.
24) In Situation 35.5, the angle formed by the plane of the movable mirror and the plane of the
image of the fixed mirror, in mrad, is closest to:
A) 36
B) 45
C) 72
D) 63
E) 54
24)
25) In Situation 35.5, the movable mirror is moved toward the observer and 12.0 fringes travel across
the field of view. The distance the movable mirror was moved, in mm, is closest to:
A) 4.5
B) 5.4
C) 3.6
D) 2.7
E) 1.8
25)
Figure 35.4
26) In Fig. 35.4, Lloyd's Mirror is an apparatus that can be used to form interference fringes using a
single source. Light from the source is reflected off a plane mirror and viewed on a screen. A
reflected ray and a direct ray can interfere to form a fringe pattern on the screen. In the
arrangement drawn here, the screen is 2.4 m from the source, and the separation between fringes
on the screen is 1.3 mm. The light has wavelength 580 nm. How high above the reflecting plane
is the source positioned?
A) 0.54 mm
B) 0.27 mm
C) 1.08 mm
D) 1.22 mm
E) 1.64 mm
6
26)
27) An oil film (n = 1.48) of thickness 290 nm floating on water is illuminated with white light at
normal incidence. What is the wavelength of the dominant color in the reflected light?
A) blue (470 nm)
B) blue-green (493 nm)
C) violet (404 nm)
D) green (541 nm)
E) yellow (572 nm)
27)
28) If light traveling in material of index n1 is reflected from a material of index n 2, then in the case
28)
where n 2 > n 1 the light undergoes a 180° phase shift on reflection. This helps us to understand
A) why a dark fringe appears on the axis (! = 0°) in a double slit interference pattern.
B) why no factor of two appears in the equation d sin ! = m!.
C) why the central spot in Newton's rings is dark.
D) why the separation of fringes due to two slit interference increases with increasing angle
of deviation.
E) why nonreflective coatings on lenses are made using coating material with a greater index
of refraction than that of the glass they are coating.
29) Light passes through a pair of very thin parallel slits. The resulting interference pattern is
viewed far from the slits at various angles ! relative to the centerline coming outward from the
midpoint between the slits. The central bright fringe is at ! = 0°, and the next bright fringes on
either side of it are at ! = ±15°. If the central bright fringe has intensity I0, the intensity of the next
29)
bright fringe on either side of it is:
A) I 0
B) I 0 cos 15°
C) I 0/2
D) I 0/ 2
E) I 0 cos2 15°
30) Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each
other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A person is
standing opposite the midpoint between the speakers and is initially 18.0 m from the midpoint.
As this person slowly walks parallel to the line connecting the speakers, at what angle ! (relative
to the centerline coming outward from the midpoint between the speakers) will he first hear no
sound?
A) 7.17°
B) 3.59°
C) 1.79°
D) 0.0626°
E) 0.125 rad
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
31) Light of wavelength 519 nm passes through two slits. In the interference pattern on a
screen 4.6 m away, adjacent bright fringes are separated by 3.9 mm. What is the
separation of the two slits?
7
31)
30)
32) Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The
liquid film is 216 nm thick, and the liquid has index of refraction 1.60. The glass has
index of refraction n = 1.50. Calculate the longest visible wavelength (as measured in
air) of the light for which there will be totally destructive interference between the rays
reflected from the top and bottom surfaces of the film. (Note: Assume that the visible
spectrum lies between 400 and 700 nm.)
32)
33) A soap bubble, when illuminated with light of 587 nm, appears to be especially
reflective. If the index of refraction of the film is 1.35, what is the thinnest thickness the
soap film can be?
33)
34) Light of wavelength ! = 525 nm passes through two slits separated by 0.500 mm and
produces an interference pattern on a screen 7.80 m away. Let the intensity at the central
maximum be Io. What is the distance on the screen from the center of this central
maximum to the point where the intensity has fallen to 1/2 I o? (Assume that the slits
are sufficiently narrow that diffraction effects may be ignored.)
34)
35) Monochromatic laser light of frequency 5.20 × 1014 Hz is shown on a pair of thin
parallel slits, and the pattern is viewed on a screen 1.20 m away. The fifth bright fringes
(not counting the central fringe) occur at ±2.12 cm on either side of the central bright
fringe. The entire apparatus is now immersed in a transparent liquid. When the
experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central
bright fringe.
(a) How far apart are the slits?
(b) What is the index of refraction of the liquid?
35)
8
Answer Key
Testname: UNTITLED4
1) E
2) E
3) A
4) E
5) C
6) E
7) E
8) C
9) D
10) B
11) A
12) E
13) C
14) A
15) D
16) B
17) E
18) E
19) D
20) B
21) E
22) A
23) D
24) E
25) D
26) A
27) E
28) C
29) A
30) B
31) 0.61 mm
32) 691 nm
33) 109 nm
34) 2.05 × 10 -3 m
35) (a) 0.163 mm
(b) 1.48
9
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
10