Deck 24: Wave Optics

Question 1

In a double-slit experiment,it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm.What happens to the distance between adjacent maxima when the slit separation is cut in half?

A)It increases to 2.0 cm.
B)It increases to 4.0 cm.
C)It decreases to 0.50 cm.
D)It decreases to 0.25 cm.
E)None of these choices are correct.

Answer 1

A

Question 2

In a single-slit diffraction experiment,the width of the slit through which light passes is reduced.What happens to the width of the central bright fringe in the resulting diffraction pattern?

A)It stays the same.
B)It becomes narrower.
C)It becomes wider.

Answer 2

C

Question 3

Monochromatic coherent light shines through a pair of slits.If the wavelength of the light is decreased,which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.)

A)The distance between the maxima stays the same.
B)The distance between the maxima decreases.
C)The distance between the minima stays the same.
D)The distance between the minima increases.
E)The distance between the minima decreases.

Answer 3

B,E

Question 4

A light beam has speed c in vacuum and speed v in a certain plastic.The index of refraction n of this plastic is

A)n = cv.
B)n = (v/c)².
C)n = v/c.
D)n = c/v.
E)n = (c/v)².

Question 5

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P.If the maximum destructive interference is to occur at point P,the two beams must travel paths that differ by

A)a whole number of wavelengths.
B)an odd number of half-wavelengths.
C)a whole number of half-wavelengths.

Question 6

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P.If the maximum constructive interference is to occur at point P,the two beams must travel paths that differ by

A)a whole number of wavelengths.
B)an odd number of half-wavelengths.
C)a whole number of half-wavelengths.

Question 7

A single-slit diffraction pattern is formed on a distant screen.Assuming the angles involved are small,by what factor will the width of the central bright spot on the screen change if the wavelength of the illuminating light is doubled?

A)It will be cut to one-quarter its original size.
B)It will be cut in half.
C)It will double.
D)It will become four times as large.
E)It will become eight times as large.

Question 8

What do we mean when we say that two light rays striking a screen are in phase with each other?

A)When the electric field due to one is a maximum, the electric field due to the other is also a maximum, and this relation is maintained as time passes.
B)They are traveling at the same speed.
C)They have the same wavelength.
D)They alternately reinforce and cancel each other.

Question 9

Monochromatic coherent light shines through a pair of slits.If the distance between these slits is decreased,which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.)

A)The distance between the maxima stays the same.
B)The distance between the maxima decreases.
C)The distance between the minima stays the same.
D)The distance between the minima increases.
E)The distance between the maxima increases.

Question 10

A beam of light traveling in air strikes a glass slab at an angle of incidence less than 90°.After entering the glass slab,what does the beam of light do? (There could be more than one correct choice.)

A)I follows the same path as before it struck the glass.
B)It follows the normal to the glass slab.
C)It bends away from the normal at the point of contact.
D)It bends closer to the normal at the point of contact.
E)It slows down.

Question 11

A single-slit diffraction pattern is formed on a distant screen.Assuming the angles involved are small,by what factor will the width of the central bright spot on the screen change if the slit width is doubled?

A)It will be cut to one-quarter its original size.
B)It will be cut in half.
C)It will double.
D)It will become four times as large.
E)It will become eight times as large.

Question 12

A double-slit interference experiment is performed in the air.Later,the same apparatus is immersed in benzene (which has an index of refraction of 1.50),and the experiment is repeated.When the apparatus is in benzene,you observe that the interference fringes are

A)more closely spaced than when the apparatus is in air.
B)equally spaced as when the apparatus is in air.
C)more widely spaced than when the apparatus is in air.

Question 13

If the diameter of a radar dish is doubled,what happens to its resolving power assuming that all other factors remain unchanged?

A)The resolving power quadruples.
B)The resolving power doubles.
C)The resolving power is cut in half.
D)The resolving power is reduced to one-quarter its original value.

Question 14

When light travels from air into water,

A)its velocity, wavelength and frequency all change.
B)its velocity changes, but its frequency and wavelength do not change.
C)its frequency changes, but its velocity and wavelength do not change.
D)its velocity and wavelength change, but its frequency does not change.
E)its wavelength changes, but its velocity and frequency do not change.

Question 15

If a sheet containing two very thin slits is heated (without damaging it),what happens to the angular location of the first-order interference minimum?

A)It moves toward the centerline.
B)It moves away from the centerline.
C)It doesn't change.

Question 16

Given perfect lenses,what is the main reason that a telescope with a large-diameter objective lens can produce a sharper image than one with a small-diameter lens?

A)A larger lens can gather more light than a smaller lens.
B)A larger lens can focus more accurately than a smaller lens.
C)There is less diffraction with a larger lens than with a smaller lens.
D)A larger lens can focus more wavelengths of light than a smaller lens.
E)A larger lens has a longer focal length than a smaller lens.

Question 17

If the index of refraction of a material is 2,this means that light travels

A)2 times as fast in air as it does in vacuum.
B)2 times as fast in the material as it does in air.
C)2 times as fast in vacuum as it does in the material.
D)2 times as fast in the material than it does in vacuum.
E)1/2 as fast in air as it does in the material.

Question 18

In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima.You observe that this separation is greatest when you illuminate the double slit with

A)blue light.
B)green light.
C)yellow light.
D)red light.
E)The separation is the same for all wavelengths.

Question 19

With what color light would you expect to be able to see the finest detail when using a microscope?

A)red, because of its long wavelength
B)yellow, because of its intermediate wavelength
C)blue, because of its shorter wavelength
D)The color does not matter.

Question 20

Two light sources are said to be coherent if they are

A)of the same frequency.
B)of the same frequency, and maintain a constant phase difference.
C)of the same amplitude, and maintain a constant phase difference.
D)of the same frequency and amplitude.

Question 21

A plastic cube is immersed in water having an index of refraction of 1.33.A laser beam in the plastic strikes the interface at an angle of 14.5° with the normal in the plastic.In the water,this beam makes an angle of 21.8° with the normal.What is the speed of light in the plastic cube? (c = 3.0 × 10⁸ m/s)

Question 22

A thin laser beam traveling in air strikes the surface of a glass plate at 41.2° with the normal.In the plate,this beam makes an angle of 22.4° with the normal.What is the speed of light in this glass?(c = 3.0 × 10⁸ m/s)

Question 23

The world's largest refracting telescope is operated at the Yerkes Observatory in Wisconsin.It has an objective lens of diameter of 1.02 m.Suppose such an instrument were mounted on a satellite at an elevation of 300 km above the ground and used to map surface details.If the telescope is forming images with light of wavelength 550 nm,what is the minimum separation of two objects on the ground whose separation could be clearly resolved by this lens?

Question 24

The speed of light in a certain material is measured to be 2.2 × 10⁸ m/s.What is the index of refraction of this material? (c = 3.0 × 10⁸ m/s)

A)1.1
B)1.2
C)1.4
D)1.6
E)1.8

Question 25

The index of refraction of a certain glass is measured to be 1.5.What is the speed of light in that glass? (c = 3.0 × 10⁸ m/s)

A)1.0 × 10⁸ m/s
B)2.0 × 10⁸ m/s
C)3.0 × 10⁸ m/s
D)4.0 × 10⁸ m/s
E)5.0 × 10⁸ m/s

Question 26

Even with perfect optics,what is the resolution limit (in radians)of the Hubble Space Telescope when it is focusing light of wavelength 400 nm? The mirror diameter is 2.4 m.

Question 27

Light having a frequency in vacuum of 6.0 × 10¹⁴ Hz enters a liquid of refractive index 2.0.What is the frequency of the light in this liquid? (c = 3.0 × 10⁸ m/s)

A)12 × 10¹⁴ Hz
B)6.0 × 10¹⁴ Hz
C)3.0 × 10¹⁴ Hz
D)1.5 × 10¹⁴ Hz
E)2.0 × 10¹⁴ Hz

Question 28

Red light with a wavelength of 650 nm travels from air into a liquid with an index of 1.33.What are the frequency and wavelength of the light in the liquid? (c = 3.0 × 10⁸ m/s)

Question 29

What is the minimum distance between two points on the Moon that could be just resolved by the Keck telescope in Hawaii using a wavelength of 600 nm and having perfect optics? The diameter of this telescope mirror system is 10 m,and the distance to the Moon is 380,000 km.

Question 30

Light of wavelength 550 nm in air is found to travel at 1.96 × 10⁸ m/s in a certain liquid.What are the frequency and wavelength of the light in this liquid? (c = 3.0 × 10⁸ m/s)

Question 31

Light having a speed in vacuum of 3.0 × 10⁸ m/s enters a liquid of refractive index 2.0.In this liquid,its speed will be

A)6.0 × 10⁸ m/s
B)3.0 × 10⁸ m/s
C)1.5 × 10⁸ m/s
D)0.75 × 10⁸ m/s
E)0.67 × 10⁸ m/s

Question 32

A light beam having a wavelength of 470 nm in air is directed into glycerine at an angle of 75.0° with the normal in air.Glycerine has a refractive index of 1.47.(c = 3.0 × 10⁸ m/s)
(a)What are the frequency and wavelength of the light in the glycerine?
(b)What angle does the light beam make with the normal in the glycerine?

Question 33

Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0.In this liquid,what is the wavelength of the light? (c = 3.0 × 10⁸ m/s)

A)1200 nm
B)600 nm
C)300 nm
D)150 nm
E)200 nm

Question 34

Treat the pupil of your eye as a circular aperture of diameter 3.5 mm.Light of wavelength 500 nm is used to view two point sources that are 283 m distant from you.How far apart must these two point sources be if they are to be just barely resolved by your eye,assuming that the resolution is limited by diffraction?

Question 35

The speed of light in a material is What is the critical angle of a light ray at the interface between the material and a vacuum?

A)24°
B)17°
C)19°
D)22°

Question 36

Light of wavelength 550 nm in air is found to travel at 1.96 × 10⁸ m/s in a certain liquid.(c = 3.0 × 10⁸ m/s)
(a)What is the index of refraction of this liquid?
(b)What is the frequency of the light in air?

Question 37

If a sheet containing a single thin slit is heated (without damaging it)and therefore expands,what happens to the width of the central bright diffraction region on a distant screen?

A)It gets narrower.
B)It gets wider.
C)It doesn't change.

Question 38

If a sheet containing a single slit is heated (without damaging it)and therefore expands,what happens to the angular location of the first-order diffraction minimum?

A)It moves toward the centerline.
B)It moves away from the centerline.
C)It doesn't change.

Question 39

A light beam with wavelength 440 nm in a certain material then enters air and its wavelength becomes 577 nm.
(a)What is the index of refraction for the material?
(b)At what angle with the plane of the surface will the light be totally reflected back into the material?

Question 40

A thick slab of plastic lies at the bottom of a tank filled with water having an index of refraction of 1.33.A narrow laser beam is shone directly downward through the water on the plastic.You then gradually rotate the laser,thereby increasing the angle with respect to the normal that it strikes the plastic.You carefully note that at the instant the beam makes an angle of 66.5° with the normal in the water,no light enters the plastic,but it did enter for angles smaller than that.What is the speed of light in the plastic slab? (c = 3.00 × 10⁸ m/s)

Question 41

Assuming a pupil diameter of 3 mm,what is the angular resolution of the human eye for light at the middle of the visible spectrum (550 nm)?

A)0.8°
B)0.2°
C)2 mrad
D)0.01°
E)2°

Question 42

A camera with a 20-cm diameter lens is recording images using a filter that allows only light of wavelength 600 nm to pass through.
(a)What is the limit on the angular resolution (in microradians)in this case?
(b)What is the diameter of the minimum-sized features that could be resolved on Mars with this camera? The distance to Mars at the time is 9.0 × 10⁷ km.

Question 43

A double-slit experiment uses coherent light of wavelength 633 nm with a slit separation of 0.100 mm and a screen placed 2.0 m away.
(a)How wide on the screen is the central bright fringe?
(b)What is the distance on the screen between first-order and second-order bright fringes?
(c)What is the angular separation (in radians)between the central maximum and the first-order maximum?

Question 44

In a two-slit experiment,a third-order bright fringe is observed at an angle of 7.10° away from the centerline.If the wavelength of light is 595 nm,how far apart are the two slits?

A)1.44 × m
B)1.07 × m
C)2.12 × m
D)2.53 × m
E)3.76 × m

Question 45

The two stars in a binary star system have an angular separation of 1.0 × 10^-5 rad.If the wavelength of the light from the system is 500 nm,what is the smallest diameter aperture telescope that could just resolve this system to show that it contains two stars?

A)0.50 cm
B)0.61 cm
C)5.0 cm
D)6.1 cm

Question 46

Suppose your telescope has perfect mirrors and is limited only by diffraction.If you are viewing with light of 400 nm wavelength,what diameter mirror in a space telescope would have 1.0-km resolution of objects on Mars when viewed from above the earth at a time when the Earth-Mars distance of 80 million kilometers?

A)39 km
B)3.9 m
C)3.9 km
D)39 m
E)390 m

Question 47

In a two-slit experiment,monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.20 × 10^-5 m.At what angle away from the centerline does the second dark fringe occur?

A)4.70°
B)3.51°
C)3.94°
D)1.17°
E)2.34°

Question 48

The pupil of a person's eye changes from a diameter of 3.5 mm to 1.5 mm as the illumination is increased.By what factor does the minimum angle of resolution change?

A)0.43
B)0.65
C)2.0
D)2.3

Question 49

In a two-slit experiment,monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.20 x m.At what angle away from the centerline does the first bright fringe occur?

A)1.56°
B)2.22°
C)3.12°
D)4.70°
E)6.24°

Question 50

What is the limiting angle of resolution for a lens of radius 2.0 mm when viewing with light having a wavelength of 600 nm?

A)1.3 × 10^-4 rad
B)1.5 × 10^-4 rad
C)1.8 × 10^-4 rad
D)1.5 × 10^-7 rad
E)1.8 × 10^-7 rad

Question 51

In one particular case,the limiting angle of resolution for an eye is 1.4 × 10^-4 rad.What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?

A)2.8 mm
B)5.6 mm
C)1.4 mm
D)8.4 mm
E)4.7 mm

Question 52

Coherent light of wavelength 519 nm passes through two slits.In the resulting interference pattern on a screen 4.6 m away,adjacent bright fringes are apart.What is the separation of the two slits?

Question 53

In a double-slit experiment,the slit separation is 1.75 mm,and two coherent wavelengths of light,425 nm and 510 nm,illuminate the slits.At what angle from the centerline on either side of the central maximum will a bright fringe from one pattern first coincide with a bright fringe from the other pattern?

Question 54

A camera used for aerial mapping has a lens with a 30-cm diameter maximum aperture and a 42-cm focal length.Light of 550 nm wavelength is used to form the image.Assuming that the resolution of the camera is limited only by diffraction,what is the smallest angle (in milliradians)subtended by an object on the ground that can be resolved by this camera at maximum aperture?

A)1.6 mrad
B)2.2 mrad
C)3.2 mrad
D)4.5 mrad
E)6.3 mrad

Question 55

In a two-slit experiment using coherent light,the distance between the slits and the screen is 1.10 m,and the distance between the slits is 0.100 mm.If the first-order bright fringe is measured to be 3.40 cm from the centerline,what is the wavelength of the light?

A)354 nm
B)241 nm
C)133 nm
D)3.09 μm
E)2.11 μm

Question 56

Coherent light of wavelength 540 nm passes through a pair of thin slits that are 3.4 × m apart.At what angle away from the centerline does the second bright fringe occur?

A)1.8°
B)3.7°
C)4.3°
D)1.5°
E)5.0°

Question 57

In a two-slit experiment,the slit separation is 3.00 × m.The interference pattern is created on a screen that is 2.00 m away from the slits.If the 7th bright fringe on the screen is 10.0 cm away from the central fringe,what is the wavelength of the light?

A)100 nm
B)204 nm
C)214 nm
D)224 nm
E)234 nm

Question 58

Astronomers are proud of their telescopes and often say they can "resolve a dime at so many miles." How many miles from a telescope mirror can you place a coin of diamete and just resolve the coin using light of wavelength (1 mi = 1.609 km)

A)19 mi
B)9.7 mi
C)40 mi
D)190,000,000 mi

Question 59

A two-slit arrangement with 60.3 μm separation between the slits is illuminated with coherent light.If a viewing screen is located 2.14 m from the slits,find the distance from the first dark fringe on one side of the central maximum to the second dark fringe on the other side.

A)52.3 mm
B)34.9 mm
C)69.7 mm
D)24.6 mm

Question 60

A certain astronomical telescope has a diameter of 5.60 m.What is the minimum angle of resolution for this telescope when it is forming images using light of wavelength 620 nm?

A)1.11 × 10^-7 rad
B)3.11 × 10^-7 rad
C)2.70 × 10^-7 rad
D)1.35 × 10^-7 rad
E)4.05 × 10^-7 rad

Question 61

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°

Question 62

A two-slit arrangement with 60.3 μm separation between the slits is illuminated with 537.0-nm wavelength light.If a viewing screen is located 2.14 m from the slits,find the distance on the screen from the first dark fringe on one side of the central maximum to the second dark fringe on the other side.

A)57.2 mm
B)38.1 mm
C)76.3 mm
D)26.9 mm

Question 63

In a double-slit experiment,the slit separation is 2.0 mm,and two wavelengths,750 nm and 900 nm,illuminate the slits.A screen is placed 2.0 m from the slits.At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?

A)1.5 mm
B)3.0 mm
C)4.5 mm
D)6.0 mm

Question 64

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

Question 65

Two radio antennas are 120 m apart on a north-south line.The two antennas radiate in phase at a frequency of 5.6 MHz.All radio measurements are made far from the antennas.What is the smallest angle,reckoned north of east from midway between the antennas,at which destructive interference of the two radio waves occurs? (c = 3.00 × 10⁸ m/s)

A)13°
B)6.4°
C)9.7°
D)16°
E)19°

Question 66

The distance between two slits is 1.50 × m.A beam of coherent light of wavelength 600 nm illuminates these slits,and the distance between the slit and the screen is 2.00 m.What is the distance on the screen between the central bright fringe and the fourth-order bright fringe?

A)0.132 m
B)0.201 m
C)0.324 m
D)0.528 m
E)0.688 m

Question 67

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 pair of slits that are apart?

A)10
B)9
C)8
D)11
E)12

Question 68

Coherent light of wavelength 575 nm falls on a double-slit and the third-order bright fringe is seen at an angle of 6.5° away from the centerline.How far apart are the double slits?

A)5.0 μm
B)10 μm
C)15 μm
D)20 μm

Question 69

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

Question 70

A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source.A fringe pattern is observed on a screen 4.8 m from the slits.If the wavelength of the monochromatic light is 450 nm,what is the angular separation between adjacent dark fringes on the screen,measured in milliradians?

A)0.15 mrad
B)0.20 mrad
C)0.25 mrad
D)0.30 mrad
E)0.36 mrad

Question 71

Two radio antennas are 10 km apart on a north-south axis on high mountain tops at the seacoast.The antennas broadcast identical AM radio signals,in phase,at a frequency of 4.70 MHz.A steamship,200 km offshore,travels toward the north at 15 km/h 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.How much later until the next occurrence of maximum reception? (c = 3.00 × 10⁸ m/s)

A)5.1 min
B)3.8 min
C)6.4 min
D)7.7 min
E)8.9 min

Question 72

A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source.A fringe pattern is observed on a screen 4.8 m from the slits.If there are 5.0 bright fringes/cm on the screen,what is the wavelength of the monochromatic light?

A)550 nm
B)600 nm
C)650 nm
D)700 nm
E)750 nm

Question 73

Two radio antennas are 130 m apart on a north-south line.The two antennas radiate in phase at a frequency of 3.6 MHz.All radio measurements are made far from the antennas.What is the smallest angle,reckoned east of north from midway between the antennas,at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s)

A)50°
B)55°
C)45°
D)40°
E)35°

Question 74

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°

Question 75

Two thin slits are 6.00 μm apart.Monochromatic coherent light falls on these slits,and produces a fifth-order bright interference fringe at an angle of 32.3° away from the centerline.What is the wavelength of the light?

A)164 nm
B)416 nm
C)614 nm
D)641 nm

Question 76

The figure shows the resulting pattern of light intensity when a single slit is illuminated by monochromatic light.The slit is 0.3 × m wide and is illuminated by light of wavelength 506 nm.A diffraction pattern is seen on a screen 2.8 m from the slit.What is the linear distance on the screen between the first two diffraction minima on either side of the central diffraction maximum?

Question 77

A single slit,which is 0.0500 mm wide,is illuminated by light of 550 nm wavelength.What is the angular separation between the first two minima on either side of the central maximum?

Question 78

An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is from the slits.If the slits are illuminated with coherent light of wavelength 633 nm,how far apart should the slits be?

A)68.5 μm
B)74.0 μm
C)79.5 μm
D)63.0 μm

Question 79

In a two-slit experiment using coherent light,the distance between the slits and the screen is 1.10 m,and the distance between the slits is 0.0400 mm.If the second order bright fringe is measured to be 4.20 cm from the centerline on the screen,what is the wavelength of light?

A)200 nm
B)381 nm
C)401 nm
D)620 nm
E)763 nm

Question 80

A double slit that is illuminated with coherent light of wavelength 644 nm produces a pattern of bright and dark fringes on a screen 6.00 cm from the slits.If the slits are 2783 nm apart,what is the distance on the screen between the 4^th and the 2^nd bright fringes on one side of the central maximum?

A)23.0 cm
B)17.6 cm
C)11.5 cm
D)3.13 cm
E)14.7 cm