Deck 27: Wave Optics

Question 1

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart.The number of fringes per unit length on the screen can be doubled

A)if the distance between the slits is doubled.
B)if the wavelength is changed to $\lambda ^ { \prime } = \frac { ? } { 2 }$ .
C)if the distance between the slits is quadruple the original distance and the wavelength is changed to $\lambda ^ { \prime } = 2 \lambda$ .
D)if any of the above occurs.
E)only if the width of the slits is changed to $w ^ { \prime } = \frac { w } { 2 }$ .

Answer 1

if any of the above occurs.

Question 2

Ray says that interference effects cannot be observed with visible light because random phase changes occur in time intervals less than a nanosecond.Stacy says that doesn't matter if collimated light from a single source reaches multiple openings.(They are arguing about a light source 50.0 cm away from two 0.010 0 mm-wide slits,2.00 mm apart,with a screen 1.00 m away from the slits. )Which one,if either,is correct,and why?

A)Ray,because the phases at the two slits will be random and different.
B)Ray,because it takes light over 3 ns to travel 1.00 m to the screen.
C)Stacy,because the difference in time of travel from the source to the slits is no more than about 7 *10 ^{- 12} s.
D)Stacy,but only if a lens is placed in front of the slits.
E)Both,because interference of light never occurs outside a physics lab.

Answer 2

Stacy,because the difference in time of travel from the source to the slits is no more than about 7 *10 ^{- 12} s.

Question 3

Light is incident on a double-slit.The fourth bright band has an angular distance of 7.0 $\degree$ from the central maximum.What is the distance between the slits (in $\mu$ m)? (Assume the frequency of the light is 5.4 *10¹⁴ Hz. )

A)27
B)21
C)24
D)18
E)14

Answer 3

18

Question 4

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart.The number of fringes per unit length on the screen can be halved

A)if the distance between the slits is changed to $d ^ { \prime } = \frac { d } { 2 }$ .
B)if the wavelength is changed to $\lambda ^ { \prime } = 2 \lambda$ .
C)if the distance between the slits is $d ^ { \prime } = 2 d$ the wavelength is changed to $\lambda ^ { \prime } = 4 \lambda$ .
D)if any of the above occurs.
E)only if the width of the slits is changed to $w ^ { \prime } = 2 w$ .

Question 5

The figures below represent interference fringes.The distances from the screen to the slits is the same for each figure,and the planes of the screen and the slits are parallel.Which figure(s)represent(s)slits with the greatest spacing d between the slits? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 6

Two slits separated by 0.050 mm are illuminated with green light ( $\lambda$ = 540 nm).How many bands of bright lines are there between the central maximum and the 12-cm position? (The distance between the double slits and the screen is 1.0 m. )

A)1111
B)111
C)11
D)1
E)11111

Question 7

A laser beam ( $\lambda$ = 694 nm)is incident on two slits 0.100 mm apart.Approximately how far apart (in m)will the bright interference fringes be on the screen 5.00 m from the double slits?

A)3.47 *10 ^{- 3}
B)3.47 * 10 ^{- 2}
C)3.47 * 10 ^{- 4}
D)3.47 *10 ^{- 6}
E)3.47 * 10 ^{- 5}

Question 8

In a double slit experiment,the distance between the slits is 0.2 mm and the distance to the screen is 100 cm.What is the phase difference (in degrees)between the waves from the two slits arriving at a point 5 mm from the central maximum when the wavelength is 400 nm? (Convert your result so the angle is between 0 and 360 $\degree$ . )

A)90 $\degree$
B)180 $\degree$
C)270 $\degree$
D)360 $\degree$
E)160 $\degree$

Question 9

Estimate the distance (in cm)between the central bright region and the third dark fringe on a screen 5.00 m from two double slits 0.500 mm apart illuminated by 500-nm light.

A)3.47
B)2.15
C)1.75
D)1.50
E)1.25

Question 10

In a double-slit experiment,the distance between the slits is 0.2 mm,and the distance to the screen is 150 cm.What wavelength (in nm)is needed to have the intensity at a point 1 mm from the central maximum on the screen be 80% of the maximum intensity?

A)900
B)700
C)500
D)300
E)600

Question 11

For small angle approximations

A)the angle must be 10 $\degree$ or less
B)the angle must be 10 radians or less
C)the angle must be 1 $\degree$ or less
D)the angle must be 1 radian or less
E)the angle must be 45 $\degree$ or less

Question 12

Two slits separated by 0.10 mm are illuminated with green light ( $\lambda$ = 540 nm).Calculate the distance (in cm)from the central bright-region to the fifth bright band if the screen is 1.0 m away.

A)2.3
B)2.5
C)2.7
D)2.1
E)2.0

Question 13

The figures below represent interference fringes.The distances from the screen to the slits is the same for each figure,and the planes of the screen and the slits are parallel.Which figure(s)represent(s)slits with the smallest spacing d between the slits? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 14

In a double slit experiment,the distance between the slits is 0.2 mm and the distance to the screen is 150 cm.What is the phase difference (in degrees)between the waves from the two slits arriving at a point P when the angular distance of P is 10 $\degree$ relative to the central peak,and the wavelength is 500 nm? (Convert your result so the angle is between 0 and 360 $\degree$ . )

A)145 $\degree$
B)155 $\degree$
C)165 $\degree$
D)135 $\degree$
E)95 $\degree$

Question 15

Two slits are illuminated with red light ( $\lambda$ = 650 nm).The slits are 0.25 mm apart and the distance to the screen is 1.25 m.What fraction of the maximum intensity on the screen is the intensity measured at a distance 3.0 mm from the central maximum?

A)0.94
B)0.92
C)0.96
D)0.98
E)0.99

Question 16

The bright and dark bands you see in a photograph of a double slit interference pattern represent

A)the respective positions of the crests and the troughs of the light wave.
B)an interference pattern that is not present unless it is produced by the camera lens.
C)the respective positions of constructive and destructive interference of light from the two sources.
D)the respective positions of destructive and constructive interference of light from the two sources.
E)the respective positions of bright and dark particles of light.

Question 17

The figure shows two point sources of light,A and B,that emit light waves in phase with each other.A is distant 3 $\lambda$ from point P.B is distant 5 $\lambda$ from P.( $\lambda$ is the wavelength. )The phase difference between the waves arriving at P from A and B is

A)0 rad.
B) $\pi$ rad.
C)2 $\pi$ rad.
D)3 $\pi$ rad.
E)4 $\pi$ rad.

Question 18

In an interference pattern,the wavelength and frequency are

A)the same in both the regions of constructive interference and the regions of destructive interference.
B)greater in regions of constructive interference than in regions of destructive interference.
C)smaller in regions of constructive interference than in regions of destructive interference.
D)unchanged in regions of destructive interference but greater in regions of constructive interference.
E)unchanged in regions of destructive interference but smaller in regions of constructive interference.

Question 19

The figure shows two point sources of light,A and B.B emits light waves that are + $\pi$ radians out of phase with the waves from A.A is 3 $\lambda$ from P.B is 5 $\lambda$ from P.( $\lambda$ is the wavelength. )The phase difference between waves arriving at P from A and B is

A)0 rad.
B) $\pi$ rad.
C)2 $\pi$ rad.
D)3 $\pi$ rad.
E)4 $\pi$ rad.

Question 20

Two slits are illuminated with green light ( $\lambda$ = 540 nm).The slits are 0.05 mm apart and the distance to the screen is 1.5 m.At what distance (in mm)from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum?

A)1
B)3
C)2
D)4
E)0.4

Question 21

Monochromatic light ( $\lambda$ = 500 nm)is incident on a soap bubble (n = 1.4)that is 50 mm thick.What is the change of phase of the light reflected from the front surface?

A)0
B)180 $\degree$
C) $\lambda$ /2
D) $\pi$ /2
E)55 $\degree$

Question 22

A film of index of refraction n₁ coats a surface with index of refraction n₂.When n₁ < n₂,the condition for destructive interference for reflected monochromatic light of wavelength $\lambda$ in air is

A) $t = m \frac { \lambda } { n _ { 1 } }$ .
B) $t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
C) $2 t = m \frac { \lambda } { n _ { 1 } }$ .
D) $2 t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
E) $4 t = m \frac { \lambda } { n _ { 1 } }$ .

Question 23

Monochromatic light ( $\lambda$ = 500 nm)is incident on a soap bubble (n = 1.40).What is the wavelength of the light (in nm)in the bubble film?

A)255
B)500
C)700
D)357
E)422

Question 24

The pupil of a cat's eye narrows to a slit width of 0.5 mm in daylight.What is the angular resolution of the cat's eye in daylight ( $\lambda$ = 500 nm)?

A)0.01 rads
B)10 ^{- 5} rads
C)10 ^{- 3} rads
D)10 ^{- 4} rads
E)0.1 rads

Question 25

A thin sheet of plastic (n = 1.60)is inserted between two panes of glass to reduce infrared ( $\lambda$ = 700 nm)losses.What thickness (in nm)is necessary to produce constructive interference in the reflected infrared radiation?

A)218
B)109
C)55
D)318
E)443

Question 26

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart.The locations of bright and dark fringes can be interchanged if a thin film is placed in front of one of the slits.The minimum thickness of this film must be

A) $d = \frac { \lambda _ { \text {aiy } } } { 2 }$ .
B) $d = \frac { \lambda _ { \text {oir } } } { 2 n _ { \text {film } } }$ .
C) $d = \frac { \lambda _ { \text {oir } } } { \left( n _ { film } - 1 \right) }$ .
D) $d = \frac { \lambda _ { \text {air } } } { 2 \left( n _ { film } - 1 \right) }$ .
E) $d = \frac { \lambda _ { \text {air } } } { n _ { \text {film } } }$ .

Question 27

How wide must a narrow slit be if the first diffraction minimum occurs at $\pm$ 12 $\degree$ with laser light of 633 nm?

A)3.0 *10 ^{- 6} m
B)3.0* 10 ^{- 5} m
C)6.1 * 10 ^{- 6} m
D)6 .1* 10 ^{- 5} m
E)1.5 *10 ^{- 6} m

Question 28

A ruby laser beam ( $\lambda$ = 694.3 nm)is sent outwards from a 2.7-m diameter telescope to the moon,384,000 km away.What is the radius of the big red spot on the moon?

A)500 m
B)250 m
C)120 m
D)1.0 km
E)2.7 km

Question 29

A film of index of refraction n₁ coats a surface with index of refraction n₂.When n₁ < n₂,the condition for constructive interference for reflected monochromatic light of wavelength $\lambda$ in air is

A) $t = m \frac { \lambda } { n _ { 1 } }$ .
B) $t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
C) $2 t = m \frac { \lambda } { n _ { 1 } }$ .
D) $2 t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
E) $4 t = m \frac { \lambda } { n _ { 1 } }$ .

Question 30

A film of index of refraction n₁ coats a surface with index of refraction n₂.When n₁ > n₂,the condition for constructive interference for reflected monochromatic light of wavelength $\lambda$ in air is

A) $t = m \frac { \lambda } { n _ { 1 } }$ .
B) $t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
C) $2 t = m \frac { \lambda } { n _ { 1 } }$ .
D) $2 t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
E) $4 t = m \frac { \lambda } { n _ { 1 } }$ .

Question 31

A narrow slit is illuminated with sodium yellow light of wavelength 589 nm.If the central maximum extends to $\pm$ 30.0 $\degree$ ,how wide is the slit?

A)0.500 mm
B)2.20*10 ^{- 6} m
C)3.33 *10 ^{- 5} m
D)1.18 $\mu$ m
E)5.89 $\mu$ m

Question 32

Monochromatic light ( $\lambda$ = 500 nm)is incident on a soap bubble (n = 1.40).How thick is the bubble (in nm)if destructive interference occurs in the reflected light?

A)102
B)179
C)54
D)1
E)89

Question 33

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart.Each bright fringe will shift to the location of the adjacent bright fringe if a thin film is placed in front of one of the slits.The minimum thickness of this film must be

A) $d = \frac { \lambda _ { \text {air } } } { 2 }$ .
B) $d = \frac { \lambda _ { \text {oir } } } { 2 n _ { \text {film } } }$ .
C) $d = \frac { \lambda _ { \text {oir } } } { \left( n _ { film } - 1 \right) }$ .
D) $d = \frac { \lambda _ { \text {air } } } { 2 \left( n _ { film } - 1 \right) }$ .
E) $d = \frac { \lambda _ { \text {air } } } { n _ { \text {film } } }$ .

Question 34

Helium-neon laser light ( $\lambda$ = 6.33 * 10 ^{- 7} m)is sent through a 0.30 mm-wide single slit.What is the width of the central maximum on a screen 1.0 m from the slit?

A)2.0 cm
B)4.2 mm
C)1.1 cm
D)2.0 mm
E)0.70 mm

Question 35

Plane waves of ultrasound,f = 51.0 kHz,impinge on a flat plane with a 1.00 cm-wide slit.What is the total angular width (2 $\theta$ )of diffracted sound waves when the speed of sound in air is 340 m/sec.

A)167 $\degree$
B)83.6 $\degree$
C)19.5 $\degree$
D)41.8 $\degree$
E)0.11 $\degree$

Question 36

The light reflected from a soap bubble (n = 1.40)appears red ( $\lambda$ = 640 nm)at its center.What is the minimum thickness (in nm)?

A)124
B)104
C)114
D)134
E)234

Question 37

Monochromatic light ( $\lambda$ = 500 nm)is incident on a soap bubble (n = 1.4)that is 500-nm thick.Calculate the change of phase of the light that penetrates the front surface,reflects from the second surface,and emerges through the first surface as an angle between 0 $\degree$ and 360 $\degree$ ?

A)280 $\degree$
B)160 $\degree$
C)220 $\degree$
D)100 $\degree$
E)290 $\degree$

Question 38

The figures below represent interference fringes.The distances from the screen to the slits is the same for each figure,and the planes of the screen and the slits are parallel.In each figure the spacing d between the slits is the same.Which figure(s)represent(s)slits illuminated with light of the greatest wavelength $\lambda$ ? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 39

The figures below represent interference fringes.The distances from the screen to the slits is the same for each figure,and the planes of the screen and the slits are parallel.In each figure the spacing d between the slits is the same.Which figure(s)represent(s)slits illuminated with light of the shortest wavelength $\lambda$ ? The white spaces represent the interference maxima.

A)I.
B)II.
C)III.
D)IV.
E)V.

Question 40

A film of index of refraction n₁ coats a surface with index of refraction n₂.When n₁ > n₂,the condition for destructive interference for reflected monochromatic light of wavelength $\lambda$ in air is

A) $t = m \frac { \lambda } { n _ { 1 } }$ .
B) $t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
C) $2 t = m \frac { \lambda } { n _ { 1 } }$ .
D) $2 t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ .
E) $4 t = m \frac { \lambda } { n _ { 1 } }$ .

Question 41

A beam of X-rays of different frequencies is reflected at 10 degrees off a crystal of interatomic spacing 0.2 nm.Which X-ray wavelength is preferentially reflected?

A)0.0943 nm
B)0.139 nm
C)0.069 5 nm
D)1.02*10^-10 m
E)3.47 *10^-11 m

Question 42

At what distance could one theoretically distinguish two automobile headlights separated by 1.5 meters? Assume a pupil diameter of 0.50 cm and yellow headlights seen at the wavelength 5.0 *10 ^{- 7} m.Assume eye fluid has an average n = 1.33.

A)6.0 km
B)12 km
C)9.0 km
D)3.0 km
E)16 km

Question 43

Which of the patterns shown below would appear on a screen when monochromatic light first passes through a narrow slit for which a = $\lambda$ and then strikes the screen? Note that the darkest area in each illustration represents the brightest area on the screen.

A)
B)
C)
D)
E)

Question 44

A helium-neon laser ( $\lambda$ = 632.8 nm)is used to calibrate a diffraction grating.If the first-order maximum occurs at 20.5 $\degree$ ,what is the line spacing,d?

A)1.81 *10^-6 m
B)1.00 *10^-5 m
C)1.00 *10^-4 m
D)1.31 *10^-6 m
E)6.76 *10^-7 m

Question 45

Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen.The darkest areas on the page represent the brightest areas on the screen.In which case is the slit illuminated with light of the shortest wavelength?

A)
B)
C)
D)
E)

Question 46

In an X-ray diffraction experiment using X-rays of $\lambda$ = 0.500 *10^-10 m,a first-order maximum occurred at 5.00 $\degree$ .Find the crystal plane spacing.

A)2.87 *10 ^{- 10} m
B)1.36 * 10 ^{- 10} m
C)6.24 *10 ^{- 9} m
D)1.93 *0 10 ^{- 9} m
E)5.74 * 10 ^{- 9} m

Question 47

A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 *10 ^{- 5} radians.If $\lambda$ = 5 *10 ^{- 7} m,what is the smallest aperture (diameter)telescope that may be used to resolve the two stars?

A)10 cm
B)5 cm
C)50 cm
D)1 m
E)4 cm

Question 48

When you look through a sheer curtain at a distant street lamp,you see a pattern of colored spots of light.This occurs by

A)polarization of light in scattering and partial absorption by the threads.
B)interference of light waves that pass through the threads with light waves that pass through the openings between the threads.
C)refraction of light waves differentially in the cylindrical threads.
D)diffraction of light waves passing through the two dimensional pattern of openings between the threads.
E)reflection of light waves by the sides of the threads.

Question 49

Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen.The darkest areas on the page represent the brightest areas on the screen.In which case is the slit illuminated with light of the longest wavelength?

A)
B)
C)
D)
E)

Question 50

When you look at a single slit diffraction pattern produced on a screen by light of a single wavelength,you see a bright central maximum and a number of maxima on either side,their intensity decreasing with distance from the central maximum.If the wavelength of the light is increased,

A)the pattern shrinks in size.(central maximum less wide;other maxima in closer to it)
B)the pattern increases in size.(central maximum wider;other maxima farther from it)
C)it does not affect the size of the pattern.
D)the width of the central maximum increases,but the other maxima do not change in position or width.
E)the width of the central maximum decreases,but the other maxima do not change in position or width.

Question 51

Each pattern shown below would appear on a screen when monochromatic light of wavelength $\lambda$ first passes through a narrow slit of width a and then strikes a screen.The darkest areas on the page represent the brightest areas on the screen.In which case does the slit have the narrowest width?

A)
B)
C)
D)
E)

Question 52

White light is spread out into spectral hues by a diffraction grating.If the grating has 1 000 lines per cm,at what angle will red light ( $\lambda$ = 640 nm)appear in first order?

A)14.7 $\degree$
B)7.35 $\degree$
C)17.7 $\degree$
D)3.67 $\degree$
E)1.84 $\degree$

Question 53

A radar installation operates at 9 000 MHz with an antenna (dish)that is 15 meters across.Determine the maximum distance (in kilometers)for which this system can distinguish two aircraft 100 meters apart.

A)7.4 km
B)370 km
C)3700 m
D)37 km
E)740 km

Question 54

When you look at a single slit diffraction pattern produced on a screen by light of a single wavelength,you see a bright central maximum and a number of maxima on either side,their intensity decreasing with distance from the central maximum.If the width of the slit is decreased,

A)the pattern shrinks in size.(central maximum less wide;other maxima in closer to it)
B)the pattern increases in size.(central maximum wider;other maxima farther from it)
C)it does not affect the size of the pattern.
D)the width of the central maximum increases,but the other maxima do not change in position or width.
E)the width of the central maximum decreases,but the other maxima do not change in position or width.

Question 55

What,approximately,are the dimensions of the smallest object on Earth that the astronauts can resolve by eye at 200 km height from the space shuttle? Assume $\lambda$ = 500 nm light and a pupil diameter D = 0.50 cm.Assume eye fluid has an average n = 1.33.

A)150 m
B)100 m
C)250 m
D)25 m
E)18 m

Question 56

The hydrogen spectrum has a red line at 656 nm,and a blue line at 434 nm.What is the first order angular separation between the two spectral lines obtained with a diffraction grating with 5000 rulings/cm?

A)7.7 $\degree$
B)16.6 $\degree$
C)6.6 $\degree$
D)3.2 $\degree$
E)19.2 $\degree$

Question 57

The large space telescope that has been placed into an Earth orbit has an aperture diameter of 2.40 meters.What angular resolution will this telescope achieve for visible light of wavelength $\lambda$ = 4.80 *10 ^{- 7} m?

A)2.44 *10 ^{- 7} rads
B)2.44 *10 ^{- 4} rads
C)2.44 *10 ^{- 3} rads
D)1.22 * 10 ^{- 6} rads
E)2.00 *10 ^{- 6} rads

Question 58

When you look at a single slit diffraction pattern produced on a screen by light of a single wavelength,you see a bright central maximum and a number of maxima on either side,their intensity decreasing with distance from the central maximum.If the width of the slit is increased,

A)the pattern shrinks in size.(central maximum less wide;other maxima in closer to it)
B)the pattern increases in size.(central maximum wider;other maxima farther from it)
C)it does not affect the size of the pattern.
D)the width of the central maximum increases,but the other maxima do not change in position or width.
E)the width of the central maximum decreases,but the other maxima do not change in position or width.

Question 59

Each pattern shown below would appear on a screen when monochromatic light of wavelength $\lambda$ first passes through a narrow slit of width a and then strikes a screen.The darkest areas on the page represent the brightest areas on the screen.In which case does the slit have the greatest width?

A)
B)
C)
D)
E)

Question 60

Monochromatic light from a He-Ne laser ( $\lambda$ = 632.8 nm)is incident on a diffraction grating containing 5 000 lines/cm.Determine the angle of the first-order maximum.

A)18.4 $\degree$
B)39.2 $\degree$
C)14.6 $\degree$
D)27.7 $\degree$
E)13.9 $\degree$

Question 61

Suppose a 5.0-meter diameter telescope were constructed on the dark side of the moon.The viewing there (except for brief periods of sunlight)would be excellent.As an example,what would be the separation between two objects that could just be resolved on the planet Mars in 500 nm light? [The distance to Mars at closest approach is 50 million miles.]

Question 62

If the interplanar spacing of NaCl is 2.814 *10^-10 m,what is the predicted angle at which X-rays of wavelength 0.140 nm will be diffracted in a first-order maximum?

A)31.3 $\degree$
B)7.20 $\degree$
C)20.5 $\degree$
D)14.4 $\degree$
E)29.8 $\degree$

Question 63

In a double-slit experiment using light of wavelength 486 nm,the slit spacing is 0.600 mm and the screen is 2.00 m from the slits.Find the distance along the screen between adjacent bright fringes.

Question 64

Nonreflective coatings for camera lenses reduce the loss of light at various surfaces of multi-lens systems,as well as preventing internal reflections that might mar the image.Find the minimum thickness of a layer of magnesium fluoride (n = 1.38)on flint glass (n = 1.66)that will cause destructive interference of reflected light of wavelength $\lambda$ = 550 nm,a wavelength which is near the middle of the visual spectrum.

Question 65

A uniform film of oil (n = 1.31)is floating on water.When sunlight in air is incident normally on the film,an observer finds that the reflected light has a brightness maximum at $\lambda$ = 450 nm and a brightness minimum at $\lambda$ = 600 nm.What is the thickness of the oil film?

Question 66

Potassium Iodide (chemical formula: KI)has a face-centered cubic structure (just like sodium chloride).If the distance between crystal planes is d = 0.353 nm and X-rays of wavelength $\lambda$ = 0.093 4 nm are used,what is the smallest angle $\theta$ at which a diffraction maximum may be obtained?

A)9.92 $\degree$
B)7.60 $\degree$
C)13.3 $\degree$
D)15.5 $\degree$
E)6.52 $\degree$

Question 67

Light from a helium-neon laser ( $\lambda$ = 632.8 nm)is incident upon a 0.200-mm wide slit.Find the total width of the central maximum 2.00 m from the slit.

Question 68

A soap bubble (n = 1.35)is floating in air.If the thickness of the bubble wall is 115 nm,what visible light wavelength is most strongly reflected?

Question 69

A diffraction grating with 4 000 lines/cm is illuminated by light from the sun.The solar spectrum is spread out on a white wall across the room.At what angle from the center line does blue light (400 nm)appear? At what angle from the center line does red light (650 nm)appear?

Question 70

Suppose a 5.0-meter diameter telescope were constructed on the dark side of the moon.The viewing there (except for brief periods of sunlight)would be excellent.As an example,what would be the separation between two objects that could just be resolved on the planet Mars in 500 nm light? [The distance to Mars at closest approach is 50 million miles.]

Question 71

Suppose two flat glass plates 30-cm long are in contact along one end and separated by a human hair at the other end.If the diameter of the hair is 50 $\mu$ m,find the separation of the interference fringes when the plates are illuminated by green light, $\lambda$ = 546 nm.

Question 72

The spacing between reflecting planes in a crystal is 2.82 * 10 ^{- 10} m.A beam of X-rays is strongly reflected at an angle of 160 $\degree$ with the crystal face.What is the wavelength of the X-rays?