Deck 17: Wave Optics

Question 1

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.The smallest angle,reckoned north of east from the antennas,at which destructive interference of the two radio waves occurs,is closest to:

A)13°
B)6.4°
C)9.7°
D)16°
E)19°

Answer 1

13°

Question 2

Situation 17.1
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.
In Situation 17.1,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)540
C)560
D)580
E)600

Answer 2

540

Question 3

A 2-slit arrangement with 60.3 μm separation between the slits is illuminated with 482.0 nm light.Assuming that 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)51.3 mm
B)34.2 mm
C)68.4 mm
D)24.1 mm

Answer 3

34.2 mm

Question 4

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)Green (541 nm)
B)Blue-green (493 nm)
C)Violet (404 nm)
D)Yellow (572 nm)
E)Blue (470 nm)

Question 5

A spectroscopist has a spectrometer equipped with a grating with 600 grooves/mm.This grating puts a 1228 nm wavelength range on a spectroscopic plate (a CCD)in order m = 5.The spectroscopist now changes the spectroscopic plate CCD by one that is larger by a factor of 3.What spectral range will be accepted when the spectroscopist observes the lines in order m = 4 with the new,larger spectroscopic plate?

A)4610 nm
B)2950 nm
C)512 nm
D)327 nm

Question 6

Light from a He-Ne laser of wavelength 633 nm passes through a circular aperture.It is observed on a screen 4.0 m behind the aperture.The width of the central maximum is 5.4 cm.What is the diameter of the hole?

A)110 μm
B)2.0 μm
C)6600 μm
D)960 μm

Question 7

A double slit illuminated with two different colors of wavelengths 831 and 558 nm forms a two-colored diffraction pattern on a screen located 228 cm away.The slit separation is 36 wavelengths of 831 nm light.(a)What order maximum for λ = 831 nm occurs near x = 20.5 cm from zeroth order? (b)What order maximum for λ = 558 nm lies close to this order?

A)(a)3 (b)5
B)(a)6 (b)10
C)(a)2 (b)2
D)(a)5 (b)3

Question 8

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.The smallest angle,reckoned east of north from the antennas,at which constructive interference of two radio waves occurs,is closest to:

A)50°
B)55°
C)45°
D)40°
E)35°

Question 9

Situation 17.1
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.
In Situation 17.1,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)410 and 700
B)430 and 720
C)450 and 740
D)470 and 760
E)490 and 780

Question 10

Situation 17.2
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.
In Situation 17.2,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)0.25
D)0.30
E)0.36

Question 11

An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is 1.70 m from the slits.If the slits are illuminated with 633 nm light,how far apart should the slits be?

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

Question 12

What is the angular separation of two spectral lines of wavelengths 417 nm and 388 nm formed in order m = 2 with a 456 line/mm grating?

A)1.63°
B)1.52°
C)0°

Question 13

A double slit illuminated with light of wavelength 644 nm forms a diffraction pattern on a screen 6 cm away.The slit separation is d = 2783 nm.What is the distance Δx between orders m = 14 and m = 9?

A)6.94 × 10⁷ nm
B)129.64 × 10⁷ nm
C)13.88 × 10⁷ nm
D)3.47 × 10⁷ nm

Question 14

How many grating grooves are needed to resolve two spectral lines at λ = 351 nm separated by 0.59 nm in order m = 4?

A)149 grooves
B)595 grooves
C)0 grooves
D)297 grooves

Question 15

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 4.70 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)3.8 min
C)6.4 min
D)7.7 min
E)8.9 min

Question 16

A single slit with width 820 nm is illuminated with light of wavelength 555 nm.How many minima occur in the angular range from θ = 0° to θ = ±26°?

A)1.3 minima
B)0.65 minima
C)1.16 minima
D)0.59 minima

Question 17

A single slit illuminated with a 500 nm light gives a diffraction pattern on a far screen with its first order minimum m = 5 at 7.00° from zeroth order.At what angle does the order m = 18 occur?

A)26.02°
B)1.94°
C)5.05°
D)0.44°

Question 18

Situation 17.2
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.
In Situation 17.2,there are 5.0 bright fringes/cm on the screen.The wavelength of the monochromatic light is closest to:

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

Question 19

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 6.77  10^-6 m?

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

Question 20

A 0.72 mm diameter hole is illuminated by infrared light of wavelength 2.5 μm What is the angle of the first dark fringe?

A)0.24 degrees
B)4.2 × 10^-3 degrees
C)1.5 × 10^-2 degrees
D)5.6 × 10^-2 degrees

Question 21

Light of wavelength 560 nm illuminates a single slit placed 60 cm from a screen.The separation between the first and third minima in the diffraction pattern is 2.8 mm.What is the slit width?

A)0.72 mm
B)0.24 mm
C)1.16 mm
D)3.8 × 10^-5 m
E)0.082 mm

Question 22

Light from sources A and B passes through the same diffraction grating and falls on a distant screen.If A produces a first-order bright spot at 30° and B produces one at 60°,then the wavelength of the light from B must be twice as great as the wavelength of the light from B.

Question 23

Two sources of light illuminate a double slit simultaneously.One has wavelength 570 nm and the second has an unknown wavelength.The m = 5 bright fringe of the unknown wavelength overlaps the m = 4 bright fringe of the light of 570 nm wavelength.What is the unknown wavelength?

A)456 nm
B)326 nm
C)380 nm
D)713 nm

Question 24

An 18 mm wide diffraction grating has rulings of 710 lines per mm.Light is incident normally on the grating.Monochromatic light of 506 nm wavelength is used.The largest angle from the normal at which an intensity maximum is formed is closest to:

A)46°
B)44°
C)42°
D)40°
E)38°

Question 25

The spacing of 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.The longest wavelength that appears in the third order spectrum is closest to:

A)590 nm
B)570 nm
C)550 nm
D)530 nm
E)610 nm

Question 26

A single slit forms a diffraction pattern,with the first minimum at an angle of 40° from central maximum.Monochromatic light of 410 nm wavelength is used.The same slit,illuminated by a different monochromatic light source,produces a diffraction pattern with the second minimum at a 60° angle from the central maximum.The wavelength of this light,in nm,is closest to:

A)276
B)293
C)309
D)326
E)342

Question 27

A single slit forms a diffraction pattern,with the first minimum at an angle of 40° from central maximum.Monochromatic light of 530 nm wavelength is used.The width of the slit,in nm,is closest to:

A)825
B)791
C)757
D)723
E)689

Question 28

Light passes through two small parallel slits and leaves an interference pattern on a distant screen.If the two slits are now moved closer to each other,the bright fringes on the screen will also move closer to each other.

Question 29

Light from a lamp,which emits light at several discreet different wavelengths,illuminates an 800 line/mm diffraction grating.A screen is placed 50.0 cm behind the grating where the light is observed.Light of wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum.What is the wavelength of the bright fringe that is 34.20 cm from the central maximum?

A)706 nm
B)783 nm
C)852 nm
D)920 nm

Question 30

In a double slit interference pattern produced by light of wavelength λ,the dark spots occur at points for which the path difference between the light from the two slits is equal to mλ/2,where m = 1,2,3,....

Question 31

Visible light passes through a hole of diameter 150 nm in a sheet of metal and falls on a distant screen.If the metal is heated,making the hole larger,the size of the central bright spot on the screen gets smaller.

Question 32

Light of wavelength 500 nm illuminates a 0.50 mm diameter hole.A screen is placed 6.0 m behind the slit.What is the width of the central maximum on the screen?

A)15 mm
B)260 μm
C)7.3 mm
D)3700 μm

Question 33

A 17 mm wide diffraction grating has rulings of 530 lines per mm.Light is incident normally on the grating.The longest wavelength that forms an intensity maximum in the fifth order is closest to:

A)377 nm
B)352 nm
C)402 nm
D)427 nm
E)452 nm

Question 34

A diffraction grating produces its first-order bright spot at an angle of 40°.If you want to reduce this angle to 20° for the same wavelength of light,you must double the line density of the grating.

Question 35

A single slit forms a diffraction pattern with monochromatic light.The fourth minimum of the pattern occurs at an angle of 32° from the central maximum.The angle at which the fifth minimum of the pattern occurs is closest to:

A)41.5°
B)41.0°
C)40.5°
D)42.0°
E)42.5°

Question 36

A grating with 396 lines/mm is illuminated with light of wavelength 343 nm.What is the angular separation between the two lines formed in order m = 2?

A)31.5°
B)15.8°
C)32.9°

Question 37

Red and blue light pass through a double slit and fall on a distant screen.The bright spots of red light will be farther from the center than the blue bright spots.

Question 38

When light passing through a diffraction grating falls on a distant screen,the interference bright spots are equally spaced along the screen.

Question 39

A single slit,1400 nm wide,forms a diffraction pattern when illuminated by monochromatic light of 490 nm wavelength.The largest angle from the central maximum at which the intensity is zero is closest to:

A)44°
B)41°
C)38°
D)35°
E)32°

Question 40

The spacing of 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.The angular width of the gap between the first order spectrum and the second order spectrum is closest to:

A)3.3°
B)4.3°
C)5.3°
D)6.3°
E)2.3°

Question 41

Explain what you see when you squeeze your eyes almost shut while looking at a small light source far away in a dark room.

Question 42

Which of the following changes would increase the separation between the bright fringes in the diffraction pattern formed by a diffraction grating?

A)Increase the wavelength of the light used.
B)Increase the separation between the slits.
C)Immerse the apparatus in water.
D)None of these
E)More than one of these

Question 43

A beam of light passes through two small parallel slits and shines on a screen.The intensity of the light at the central bright spot on this screen will be twice as bright as the intensity of light coming from each hole.

Question 44

What is the general rule for deciding whether we add amplitudes and then square to get the final intensity or first square each amplitude and add to get the final intensity?

Question 45

Why are only about 6-10 minima seen when light illuminates a single slit?

Question 46

What is the difference between diffraction and interference?

Question 47

Two identical gratings are put together to make one grating twice as wide.What condition must be fulfilled so that the resolution truly doubles?

Question 48

A diffraction grating is described by its groove spacing d.But each groove consists of a clear aperture a and an opaque part b.For fixed d how does changing a and b (the ratio a/b)affect the diffracted light?

Question 49

How wide is a single slit that gives its first minimum at 90°?

Question 50

A single slit gives destructive interference when ml = w sin θ.A double slit gives constructive interference when ml = d sin θ.Explain the role of d and w for the single and double slit.

Question 51

A diffraction pattern of a single slit is compared to the diffraction pattern from a circular aperture of diameter r = w.Are they similar,equal?