35) Using monochromatic light of 410 nm wavelength, a single thin slit forms a diffraction
pattern, with the first minimum at an angle of 40.0° from central maximum. The same slit, when
illuminated by a new monochromatic light source, produces a diffraction pattern with the second
minimum at a 60.0° angle from the central maximum. What is the wavelength of this new light?
A) 276 nm
B) 293 nm
C) 309 nm
D) 326 nm
E) 342 nm
36) A single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0°
from central maximum. If monochromatic light of 530.0-nm wavelength is used for the
illumination, what is the width of the slit?
A) 825 nm
B) 791 nm
C) 757 nm
D) 723 nm
E) 689 nm
37) A single slit, 1400 nm wide, forms a diffraction pattern when illuminated by monochromatic
light of 490-nm wavelength. What is the largest angle from the central maximum at which the
intensity of the light is zero?
A) 44°
B) 41°
C) 38°
D) 35°
E) 32°
38) A single thin slit forms a diffraction pattern when illuminated with monochromatic light. The
fourth minimum of the pattern occurs at an angle of 32.0° away from the central maximum. At
what angle does the fifth minimum occur?
A) 41.5°
B) 41.0°
C) 40.5°
D) 42.0°
E) 42.5°
39) A beam of monochromatic light passes through a slit that is 11.0 μm wide. If the first order
dark fringe of the resulting diffraction pattern is at an angle of 4.31° away from the centerline,
what is the wavelength of light?
A) 827 nm
B) 301 nm
C) 602 nm
D) 402 nm
E) 201 nm
40) A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide. At what
the angle away from the centerline does the first dark fringe occur?
A) 9.35°
B) 11.4°
C) 12.2°
D) 39.9°
E) 18.7°
41) A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide. At what
the angle away from the centerline does the second dark fringe occur?
A) 11.4°
B) 9.35°
C) 12.2°
D) 39.9°
E) 18.7°
42) A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10-5 m wide, and
then goes on to a screen that is 2.2 m from the slit. On the screen, how far is the second dark
fringe from the center of the diffraction pattern?
A) 3.9 cm
B) 4.2 cm
C) 6.3 cm
D) 2.1 cm
E) 8.5 cm
43) When light of wavelength 450 nm falls on a single slit of width 0.30 mm, what is the
angular width of the central bright region?
A) 0.086°
B) 0.13°
C) 0.17°
D) 0.26°
E) 0.35°
44) When a single slit that is 0.050 mm wide is illuminated by light of 550-nm wavelength, what
is the angular separation between the first two minima on one side of the central maximum?
A) 0.36°
B) 0.47°
C) 0.54°
D) 0.63°
E) 1.3°
45) Light of wavelength 687 nm passes through a single slit that is 0.75 mm wide. At what
distance from the slit should a screen be placed so that the second dark fringe in the diffraction
pattern is to be 1.7 mm from the center of the pattern?
A) 0.39 m
B) 0.93 m
C) 1.1 m
D) 1.5 m
E) 1.9 m
46) Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is
viewed on a screen that is 1.5 m from the slit. What is the width on the screen of the central
maximum?
A) 0.34 cm
B) 0.68 cm
C) 0.92 cm
D) 1.2 cm
E) 1.5 cm
47) Light of wavelength 580 nm is incident on a slit of width 0.30 mm. An observing screen is
placed 2.0 m past the slit. Find the distance on the screen of the first order dark fringe from the
center of the pattern.
A) 0.26 mm
B) 1.5 mm
C) 1.9 mm
D) 3.9 mm
E) 7.7 mm
48) A beam of light of wavelength 630 nm is incident on a slit that is 0.400 mm wide. If the
distance between the slit and the screen is 1.80 m, what is the width on the screen of the central
bright fringe?
A) 1.94 mm
B) 2.94 mm
C) 3.54 mm
D) 5.67 mm
E) 6.94 mm
49) A diffraction grating is to be used to find the wavelength of the emission spectrum of a gas.
The grating spacing is not known, but light of a known wavelength of 632.8 nm is deflected by
43.2° in the second order by this grating. Light of the wavelength to be measured is deflected by
34.9° in the second order. What is the wavelength of the light that is to be measured?
50) When red light illuminates a grating with 7000 lines per centimeter, its second maximum is
at 62.4°. What is the wavelength of this light?
51) A diffraction grating has 5150 lines per centimeter ruled on it. What is the angular separation
between the first- and the third-order bright spots on the same side of the central maximum when
the grating is illuminated by a beam of light with wavelength 633 nm?
52) In a diffraction grating experiment, light of 600 nm wavelength produces a first-order
maximum 0.35 mm from the central maximum on a distant screen. On the same screen, a second
monochromatic source produces a third-order maximum 0.87 mm from the central maximum
when it passes through the same diffraction grating. What is the wavelength of the light from the
second source?
53) Consider an experiment using a diffraction grating with 7000 lines/cm, a screen 2.50 m
away, and a wavelength beam of light.
(a) How many side maxima will be observed on one side of the central maximum?
(b) How far apart on the screen are the first-order and second-order maxima on the same side of
the central maximum?
54) What is the angular separation of two spectral lines of wavelengths 497 nm and 251 nm
formed in the third order with a diffracting grating having 587 lines per millimeter?
A) 34.8°
B) 24.8°
C) 41.3°
D) 29.4°
E) 4.21°
55) A diffraction grating with 396 lines/mm is illuminated with light of wavelength 343 nm.
What is the angular separation between the two second-order bright fringes?
A) 31.5°
B) 15.8°
C) 32.9°
56) Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating. If
the third-order maximum of the diffraction pattern is observed at 32° from the centerline, what is
the distance between the slits of the grating?
A) 0.93 μm
B) 1.4 μm
C) 2.8 μm
D) 8.5 μm
57) Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating. If
the third-order maximum of the diffraction pattern is observed at 32.0°, what is the total number
of maxima can be seen?
A) 5
B) 7
C) 10
D) 11
E) 8
58) An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Monochromatic
light of wavelength 506 nm wavelength is incident normally on the grating. What is the largest
angle from the centerline at which an intensity maximum is formed?
A) 46°
B) 44°
C) 42°
D) 40°
E) 38°
59) When light illuminates a diffraction grating with 7000 lines per centimeter, its second order
maximum is at 62.4°. What is the wavelength of the light?
A) 336 nm
B) 363 nm
C) 633 nm
D) 752 nm
60) When a diffraction grating having 5000 lines/cmis illuminated by monochromatic light, the
angle between the central maximum and the fourth order maximum is 47.2°. What is the
wavelength of the light?
A) 138 nm
B) 183 nm
C) 367 nm
D) 637 nm
61) Monochromatic light is incident on a diffraction grating that is 75 mm wide and ruled with
50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the
incident light?
A) 202 nm
B) 403 nm
C) 605 nm
D) 806 nm
62) A diffraction grating has 6.00 × 103 lines per centimeter ruled on it. What is the angular
separation between the second and the third orders on the same side of the central order when the
grating is illuminated with a beam of light of wavelength 550 nm?
A) 20.5°
B) 30.5°
C) 40.6°
D) 50.5°
63) A 17-mm-wide diffraction grating has rulings of 530 lines per millimeter. White light is
incident normally on the grating. What is the longest wavelength that forms an intensity
maximum in the fifth order?
A) 377 nm
B) 352 nm
C) 402 nm
D) 427 nm
E) 452 nm
64) What is the slit spacing of a diffraction grating necessary so that 600-nm light will produce a
first order principal maximum at 25.0° away from the centerline?
A) 1.42 μm
B) 2.01 μm
C) 3.12 μm
D) 4.12 μm
E) 5.44 μm
65) A beam of light of wavelength 600 nm is incident normally on a diffraction grating with a
spacing between slits of 1.70 × 10-4 cm. At what angle away from the centerline does a first-
order maximum occur?
A) 10.5°
B) 12.1°
C) 16.4°
D) 18.2°
E) 20.7°
66) The distance between the ruled lines on a diffraction grating is 1900 nm. The grating is
illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm
wavelength band. What is the angular width of the gap between the first order spectrum and the
second order spectrum?
A) 3.3°
B) 4.3°
C) 5.3°
D) 6.3°
E) 2.3°
67) The distance between the ruled lines on a diffraction grating is 1770 nm. The grating is
illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm
wavelength band. What is the longest wavelength that appears in the third order spectrum?
A) 590 nm
B) 570 nm
C) 550 nm
D) 530 nm
E) 610 nm
68) A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This
sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is
incident normally on the sheet. If the microwave wavelength is 6.0 cm, what is the largest angle
from the normal, at which an intensity maximum occurs?
A) 64°
B) 69°
C) 74°
D) 79°
E) 84°
69) A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This
sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is
incident normally on the sheet. What is the smallest microwave frequency for which only the
central maximum will occur? (c = 3.00 × 108 m/s)
A) 0.50 GHz
B) 0.70 GHz
C) 1.0 GHz
D) 1.5 GHz
E) 2.0 GHz
70) A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This
sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is
incident normally on the sheet. If the intensity maxima occur 2.0° apart in the central region,
what is the wavelength of the microwaves?
A) 5.0 mm
B) 6.0 mm
C) 7.0 mm
D) 8.0 mm
E) 9.0 mm
71) A diffraction grating has 450 lines per millimeter. What is the highest order m that contains
the entire visible spectrum from 400 nm to 700 nm?
A) m = 2
B) m = 3
C) m = 4
D) m = 5
E) m = 6
72) Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The
liquid film is thick, and the liquid has index of refraction 1.60. The glass has index of
refraction 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. Assume that the visible spectrum lies between 400 nm and 700 nm.
73) A soap bubble, when illuminated at normal incidence with light of 463 nm, appears to be
especially reflective. If the index of refraction of the film is 1.35, what is the minimum thickness
the soap film can be if it is surrounded by air?
74) Light in air of wavelength 500 nm illuminates a soap film that has an index of refraction of
1.3 and air on both sides. What is the minimum thickness of this film that will produce
cancellation in the reflected light when the light is incident normally on the film?
75) A soap bubble with air on both sides has an index of refraction of 1.33. What minimum
thickness of the wall of this bubble will ensure maximum reflectance of normally incident light
having a wavelength of 530 nm?
76) A glass plate that is 2.5 cm long is separated from another glass plate at one end by a strand
of someone’s hair that is 0.010 mm in diameter. How far apart are the adjacent interference
bands when viewed with light of wavelength 600 nm?
77) The wavelength of light in a thin film is 360 nm and the wavelength of light in vacuum is
469 nm. What is the index of refraction for the film?
A) 1.10
B) 1.30
C) 1.50
D) 1.70
E) 1.90
78) Light has a wavelength of 600 nm in a vacuum. It passes into glass, which has an index of
refraction of 1.50. What is the wavelength of the light in the glass?
A) 600 nm
B) 500 nm
C) 400 nm
D) 300 nm
E) 900 nm
79) Light has wavelength 600 nm in a vacuum. It passes into glass, which has an index of
refraction of 1.5. What is the frequency of the light inside the glass? (c = 3.0 × 108 m/s)
A) 3.3 × 1014 Hz
B) 5.0 × 1014 Hz
C) 3.3 × 105 Hz
D) 5.0 × 105 Hz
80) A 360-nm thick oil film floats on the surface of a pool of water water. The indices of
refraction of the oil and the water are 1.5 and 1.33, respectively. When the surface of the oil is
illuminated from above at normal incidence with white light, what are the two wavelengths of
light between 400 nm to 800 nm wavelength that are most strongly reflected?
A) 410 nm and 700 nm
B) 430 nm and 720 nm
C) 450 nm and 740 nm
D) 470 nm and 760 nm
E) 490 nm and 780 nm
81) A 360-nm thick oil film floats on the surface of a pool of water. The indices of refraction of
the oil and the water are 1.50 and 1.33, respectively. When the surface of the oil is illuminated
from above at normal incidence with white light, what is the wavelength of light between 400
nm to 800 nm wavelength that is most weakly reflected?
A) 520 nm
B) 540 nm
C) 560 nm
D) 580 nm
E) 600 nm
82) A light beam with wavelength 500 nm is reflected constructively from a thin layer of oil
having index of refraction 1.25. The oil floats on the top of water of index of refraction 1.33.
What is the minimum thickness of the layer of oil?
A) 100 nm
B) 150 nm
C) 175 nm
D) 200 nm
E) 225 nm
83) A 500-nm-wavelength beam of light illuminates a soap film with air on both sides and an
index of refraction 1.33. If the beam of light is incident normally on the film, what is the
minimum thickness of the film to make the reflected light enhanced in brightness?
A) 47.0 nm
B) 74.0 nm
C) 94.0 nm
D) 152 nm
E) 268 nm
84) What is the minimum thickness of a soap bubble film with refractive index 1.38 that results
in a constructive interference in the reflected light if this film is illuminated by a beam of light of
wavelength 610 nm?
A) 222 nm
B) 111 nm
C) 333 nm
D) 444 nm
E) 555 nm
85) A soap bubble has an index of refraction of 1.33. What minimum thickness of this bubble
will ensure maximum reflectance of normally-incident light having a wavelength of 530 nm?
A) 24.9 nm
B) 76.9 nm
C) 99.6 nm
D) 199 nm
E) 398 nm
86) An oil film with refractive index 1.48 and thickness 290 nm is floating on water and
illuminated with white light at normal incidence. What is the wavelength of the dominant color
in the reflected light?
A) green (541 nm)
B) blue-green (493 nm)
C) violet (404 nm)
D) yellow (572 nm)
E) blue (470 nm)
87) A sodium light, having wavelength 589.3 nm, is used to view a soap film to make it look
black when directed perpendicular to the film. What is the minimum thickness of the soap film if
the index of refraction of soap solution is 1.38?
A) 114 nm
B) 194 nm
C) 294 nm
D) 314 nm
E) 214 nm
88) A soap bubble film that is 106 nm thick and has an index of refraction of 1.42 results in
constructive interference in the reflected light if this film is illuminated by a beam of light with a
wavelength of 601 nm. What are the next three thicknesses of this film that will also result in
constructive interference?
A) 212 nm, 318 nm, 424 nm
B) 53.0 nm, 35.3 nm, 26.5 nm
C) 212 nm, 424 nm, 636 nm
D) 67.0 nm, 42.4 nm, 22.3 nm
E) 318 nm, 530 nm, 742 nm
89) A puddle of water has a thin film of gasoline floating on it. A beam of light is shining
perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the
indices of refraction of gasoline and water are 1.40 and 1.33, respectively, what must be the
minimum thickness of the film to see a bright reflection?
A) 100 nm
B) 200 nm
C) 300 nm
D) 400 nm
E) 500 nm
90) A piece of glass has a thin film of gasoline floating on it. A beam of light is shining
perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the
indices of refraction of gasoline and glass are 1.40 and 1.50, respectively, what is the minimum
nonzero thickness of the film to see a bright reflection?
A) 500 nm
B) 400 nm
C) 300 nm
D) 200 nm
E) 100 nm
91) Two very 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 refractive index of the glass plates is 1.55. The plates are illuminated at normal incidence
with monochromatic light, and fringes are observed. When the monochromatic light has a
wavelength of 580 nm, how many bright fringes are visible in the pattern?
A) 60
B) 70
C) 80
D) 90
E) 100
92) Two very 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 refractive index of the glass plates is 1.55. The plates are illuminated at normal incidence
with monochromatic light, and fringes are observed. If the spacing of the dark fringes is 2.0 mm,
what is the wavelength of the monochromatic light?
A) 425 nm
B) 475 nm
C) 525 nm
D) 675 nm
E) 725 nm
93) A thin uniform film of oil that can be varied in thickness covers a sheet of glass of refractive
index 1.52. The refractive index of the oil is 1.64. Light of wavelength 555 nm is shone from air
at normal incidence on the film. Starting with no oil on the glass, you gradually increase the
thickness of the oil film until the first interference maximum in the reflected light occurs. What
is the thickness of the oil film at that instant?
A) 139 nm
B) 169 nm
C) 183 nm
D) 84.6 nm
E) 91.3 nm
94) Light of wavelength 500 nm illuminates a round 0.50-mm-diameter hole. A screen is placed
6.0 m past the slit. What is the width of the central bright circle on the screen?
A) 15 mm
B) 260 μm
C) 7.3 mm
D) 3700 μm
95) Light from a He-Ne laser of wavelength 633 nm passes through a circular aperture. The
resulting pattern is observed on a screen 4.0 m behind the aperture, where the width of the
central bright circle is 1.1 cm. What is the diameter of the hole?
A) 560 μm
B) 9.8 μm
C) 32,000 μm
D) 4700 μm
96) A round 0.85-mm–diameter hole is illuminated by infrared light of wavelength 2.5 μm What
is the angle of the first dark fringe in the resulting pattern?
A) 0.21 degrees
B) 3.6 × 10-3 degrees
C) 1.2 × 10-2 degrees
D) 4.8 × 10-2 degrees