Deck 25: Interference and Diffraction

Question 1

A thin film of soapy water, n = 1.37, is held vertical.Light of wavelength 600 nm is reflected from the film and horizontal dark lines appear.What is the thinnest soap film for which a bright band will occur?

A) 150 nm
B) 109 nm
C) 90.0 nm
D) 438 nm
E) 219 nm

Answer 1

109 nm

Question 2

A thin film of magnesium fluoride (n = 1.38) is applied to glass (n = 1.50) at a thickness of 100 nm.For what visible wavelength will this coating act as nonreflecting?

A) 600 nm
B) 578 nm
C) 552 nm
D) 504 nm
E) 491 nm

Answer 2

552 nm

Question 3

Coherent light of a single frequency passes through a double slit with a separation d,to produce a pattern on a screen as distance D from the slits.What would cause the separation between adjacent minima on the screen to increase?

A) increase the index of refraction of the medium in which the setup is immersed
B) increase the separation d between the slits
C) increase the distance D
D) increase the frequency of the incident light

Answer 3

increase the distance D

Question 4

In a double slit experiment,the intensity of the light reaching the center of he screen from one slit alone is I₀ and intensity of the light reaching the center from the other slit alone is 9I₀.When both slits are open,what is the intensity of the light at the minima nearest the center?

A) 4I₀
B) 0
C) 8I₀
D) 2I₀

Question 5

Wave 1 has amplitude of 9.0 units and wave 2 has amplitude 4.0 units.What is the ratio of their intensities,I₁/I₂?

A) 20
B) 5.1
C) 2.3
D) 1.5
E) 1.3

Question 6

Two coherent waves,each with intensity I₀,reach the same point in phase.The amplitude of the superposed wave is _________.

A) 0
B) I₀
C) 2I₀
D) 3I₀
E) 4I₀

Question 7

A general condition that two waves undergo constructive interference is that

A) their phase difference is zero.
B) their phase difference is $\pi$ /2 rad.
C) their phase difference is $\pm\pi$ /2 rad.
D) their phase difference is an even integral multiple of $\pi$ rad.
E) their phase difference is an odd integral multiple of $\pi$ rad.

Question 8

Wave 1 has intensity 9.0 units while wave 2 has intensity 4.0 units.What is their ratio of amplitudes,A₁/A₂?

A) 20
B) 5.1
C) 2.3
D) 1.5
E) 1.3

Question 9

What is the minimum thickness of a coating of magnesium fluoride (n = 1.38) applied to glass (n = 1.50) that gives a minimum reflection for 600 nm light?

A) 600 nm
B) 300 nm
C) 435 nm
D) 109 nm
E) 100 nm

Question 10

A thin film of soapy water, n = 1.37, is held vertical.Light of wavelength 600 nm is reflected from the film and horizontal dark lines appear.What is the difference in thickness of the soap film from one band to the next?

A) 600 nm
B) 438 nm
C) 300 nm
D) 219 nm
E) 900 nm

Question 11

Two coherent waves reach the same point in phase.One wave has an intensity of 8.00 units and the other has an intensity of 4.00 units.What is the intensity of the superposed wave?

A) 4.00 units
B) 8.00 units
C) 12.0 units
D) 23.3 units
E) 24.0 units

Question 12

What minimum thickness of oil (n = 1.50) on the surface of water (n = 1.33) would give destructive interference for 550 nm light with normal incidence?

A) 275 nm
B) 183 nm
C) 92.0 nm
D) 80.0 nm
E) 78.0 nm

Question 13

If two coherent waves,one with intensity 8.0 units and the other with intensity 4.0 units,undergo destructive interference,what is the resulting intensity?

A) 4.0 units
B) 6.0 units
C) -4.0 units
D) 1.9 units
E) 0.7 units

Question 14

Two coherent waves reach the same point in phase.One wave has amplitude 8 units and the other has amplitude 6 units.The amplitude of the superposed wave is ______ units.

A) 6
B) 8
C) 10
D) 14
E) 2

Question 15

What minimum thickness of oil (n = 1.50) on the surface of water (n = 1.33) would give constructive interference for 550 nm light with normal incidence?

A) 78.0 nm
B) 80.0 nm
C) 92.0 nm
D) 183 nm
E) 275 nm

Question 16

Using a Michelson interferometer and a light source of 400 nm,a change from bright to dark indicates a change in distance of

A) 2.0 $\times$ 10^-4 mm.
B) 4.0 $\times$ 10^-4 mm.
C) 3.0 $\times$ 10^-4 mm.
D) 1.0 $\times$ 10^-4 mm.

Question 17

Two coherent sources emit waves of 2.0-m wavelength in phase.If the path length to an observer differs by ________,then _________ interference occurs.

A) 1.0 m,constructive
B) 2.0 m,destructive
C) 3.5 m,constructive
D) 7.0 m,destructive
E) 8.0 m,destructive

Question 18

What is the minimum thickness of the air layer between two flat glass surfaces if the glass is to appear bright when 450 nm light is incident normally?

A) 57.0 nm
B) 113 nm
C) 170 nm
D) 226 nm

Question 19

A Michelson interferometer is set up for microwaves.Initially the reflectors are placed so the detector reads a maximum.When one of the reflectors is moved 12 cm,the reading goes from a minimum to a maximum six times.What is the wavelength of the microwaves?

A) 0.5 cm
B) 4 cm
C) 1 cm
D) 2 cm

Question 20

A general condition that two waves undergo destructive interference is

A) their phase difference is zero.
B) their phase difference is $\pi$ /2 rad.
C) their phase difference is $\pm\pi$ /2 rad.
D) their phase difference is an even integral multiple of $\pi$ rad.
E) their phase difference is an odd integral multiple of $\pi$ rad.

Question 21

Increasing the wavelengths in a double-slit experiment has what effect on the position of maxima on a screen at fixed distance?

A) none
B) maxima get closer together
C) maxima get farther apart
D) maxima get cancelled by minima
E) maxima pass minima on the screen

Question 22

What slit separation would a grating have to produce a first-order maximum at an angle of 40.0 $^{\circ}$ for a wavelength of 589 nm?

A) 109 nm
B) 690 nm
C) 378 nm
D) 458 nm
E) 916 nm

Question 23

In a double-slit interference pattern,the third maximum from the central maximum corresponds to which value of m?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 24

If the two 2^nd order maxima (m = 2) are separated by 2.0 cm on the screen in a double-slit experiment,what is the separation of the m = 3 minima? Assume the angle is very small.

A) 1.5 cm
B) 2.0 cm
C) 2.5 cm
D) 3.0 cm
E) 3.5 cm

Question 25

In a Young's double slit experiment,a 5^th order maximum occurs at an angle of 1.422 $^{\circ}$ .If the screen is 3.90 m from the slits and the slit separation is 0.135 mm,what wavelength is being used?

A) 335 nm
B) 670 nm
C) 476 nm
D) 589 nm
E) 690 nm

Question 26

In a double-slit experiment,when both interference and diffraction are taken into account,which is the lowest order maximum that is missing in the case where the slit separations is 0.020 mm and the slit widths are each 0.005 mm?

A) 1
B) 2
C) 3
D) 4
E) no order is missing

Question 27

A laser beam is shown through a grating and a first-order maximum is produced at an angle of 25 $^{\circ}$ .At what angle is the second-order maximum produced?

A) 75 $^{\circ}$
B) 58 $^{\circ}$
C) 50 $^{\circ}$
D) 35 $^{\circ}$
E) 27 $^{\circ}$

Question 28

A laser beam is shown through a grating and the first-order maximum is produced at 17 $^{\circ}$ .What is the highest order maximum that can be produced by this arrangement?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 29

A double-slit experiment is performed and then redone using slits of double the previous separation.Nothing else is changed.If the approximation sin $\theta$ $\approx$ $\theta$ holds,what happens to the angle between the maxima?

A) it stays the same
B) it doubles
C) it quadruples
D) it halves
E) it quarters

Question 30

For an angle of 10 degrees,what is the percent difference in sin $\theta$ and $\theta$ in radians?

A) 0.1%
B) 0.3%
C) 0.5%
D) 0.7%
E) more than 1%

Question 31

Substituting tan $\theta$ for sin $\theta$ results in what percent error for an angle of 5.00 $^{\circ}$ ?

A) 5.00
B) 0.0166
C) 0.0333
D) 0.191
E) 0.381

Question 32

What is the highest order maximum that is possible when using a grating with 600 slits per mm for a wavelength of 700 nm?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 33

If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm,what angle separates the two 4^th order maxima?

A) 0.768 $^{\circ}$
B) 3.07 $^{\circ}$
C) 0.307 $^{\circ}$
D) 1.54 $^{\circ}$
E) 0.154 $^{\circ}$

Question 34

A Young's double-slit experiment is performed and then repeated after moving the screen to triple the previous distance from the slit.What happens to the angular separation (as measured from the slits)of the 4^th order maxima?

A) there is no change
B) it becomes one-third the original value
C) it becomes four times the original value
D) it triples
E) it increases by a factor of 2.25

Question 35

Light of wavelength 450 nm produces a first-order maximum at 27 $^{\circ}$ when viewed through a grating.At what angle would a first order maximum occur for a wavelength of 600 nm viewed through this grating?

A) 54 $^{\circ}$
B) 40 $^{\circ}$
C) 36 $^{\circ}$
D) 37 $^{\circ}$
E) 14 $^{\circ}$

Question 36

Using a double-slit with a d = 300 nm and light of a wavelength of 400 nm,what would you see on a distant screen?

A) the intensity is maximum at the center and gradually decreases to either side
B) the intensity is minimal at the center and gradually increases to either side
C) the intensity is maximum in a single narrow line at the center
D) the intensity is minimal in a single narrow line at the center

Question 37

Laser light of 589 nm wavelength is shown through parallel slits forming a series of maxima on a screen 4.20 m away.If the distance between the central maximum and the first order maximum is 1.67 cm,what is the slit separation?

A) 3.90 $\times$ 10^-3 cm
B) 3.98 $\times$ 10^-3 m
C) 9.98 $\times$ 10^-5 m
D) 1.40 $\times$ 10^-3 m
E) 1.48 $\times$ 10^-4 m

Question 38

A grating is made with 600 slits per millimeter.What is the slit separation?

A) 600 nm
B) 1.67 $\times$ 10^-6 m
C) 3.33 $\times$ 10^-6 m
D) 160 pm
E) 916 nm

Question 39

For an angle of one degree,to how many significant figures do sin $\theta$ and $\theta$ (in radians) agree?

A) 3
B) 4
C) 5
D) 6
E) 7

Question 40

A grating with 8000 slits space over 2.54 cm is illuminated by light of a wavelength of 546 nm.What is the angle for the third order maximum?

A) 31.1 $^{\circ}$
B) 15.1 $^{\circ}$
C) 26.3 $^{\circ}$
D) 10.5 $^{\circ}$

Question 41

Two point sources of light of wavelength 600 nm are being viewed by a telescope of aperture width 2.0 cm.What is the closest angular separation at which the two sources can be resolved?

A) 7.3 $\times$ 10^-5 rad
B) 3.7 $\times$ 10^-5 rad
C) 7.3 $\times$ 10^-5 deg
D) 3.7 $\times$ 10^-5 deg
E) 4.2 $\times$ 10^-3 deg

Question 42

Holograms appear three dimensional because

A) they are in color.
B) they are transparent.
C) they consist of Young double slits.
D) they recreate wave fronts as if they came from the original source.
E) of their spectral response to refraction.

Question 43

If the eye can resolve points separated by 2.20 $\times$ 10^-4 rad,when viewed at 12.0 inches,how many dpi is this? (dpi = dots per inch)

A) 250
B) 340
C) 380
D) 400
E) 590

Question 44

A single slit of width 0.030 mm is used to project a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit.What is the width of the central maximum?

A) 1.7 cm
B) 3.3 cm
C) 6.7 cm
D) 1.5 mm
E) 3.0 mm

Question 45

The resolution of a microscope can be most improved by

A) increasing the wavelength and diameter of the lens.
B) decreasing the wavelength and the diameter of the lens.
C) decreasing the wavelength and increasing the diameter of the lens.
D) increasing the wavelength and decreasing the diameter of the lens.

Question 46

What is the angular resolution of the eye at a wavelength of 500 nm for a pupil diameter of 2.8 mm?

A) 1.8 $\times$ 10^-4 rad
B) 2.2 $\times$ 10^-4 rad
C) 8.9 $\times$ 10^-5 rad
D) 4.5 $\times$ 10^-5 rad
E) 3.3 $\times$ 10^-5 rad

Question 47

X-rays of fixed wavelength yield a first-order maximum at a grazing angle of 12 $^{\circ}$ .At what angle would one expect to find the corresponding 3^rd order maximum?

A) 4.0 $^{\circ}$
B) 12 $^{\circ}$
C) 36 $^{\circ}$
D) 39 $^{\circ}$
E) more information is needed

Question 48

White light is shone on a very thin layer of mica (n = 1.57).When the mica layer is observed from the illuminated side,interference maxima for wavelengths of blue (480 nm) and yellow (560 nm)are observed.What is the thickness of the mica layer?

A) 1.58 $\mu$ m
B) 0.79 $\mu$ m
C) 3.16 $\mu$ m
D) insufficient information is given.

Question 49

Max von Laue is known for his work with

A) double-slit interference.
B) single-slit diffraction.
C) x-ray crystallography.
D) holography.
E) magnetic resonance imaging.

Question 50

For a plane wave approaching an obstacle with a rectangular opening,diffraction becomes important in which of the following circumstances?

A) the beam is coherent
B) one or more dimensions of the rectangular opening is near the wavelength of the source
C) both dimensions of the rectangular opening are larger than the wavelength of the source
D) only if the opening is circular

Question 51

Holography was invented by

A) Max von Laue.
B) Sir David Brewster.
C) Rosalind Franklin.
D) Dennis Gabor.
E) Bill Gates.

Question 52

In a single-slit experiment,light of wavelength 500 nm is used to produce a diffraction pattern on a screen 4.0 m away.If the distance between both 3^rd order minima is 6.0 cm,what is the slit width?

A) 2.0 $\times$ 10^-4 m
B) 1.0 $\times$ 10^-4 m
C) 4.0 $\times$ 10^-4 m
D) 0.67 $\times$ 10^-4 m
E) 0.44 $\times$ 10^-4 m

Question 53

If a laser printer prints at 600 dots per inch,what is their angular separation when viewed from 40 cm?

A) 4.2 $\times$ 10^-5 rad
B) 2.7 $\times$ 10^-4 rad
C) 1.1 $\times$ 10^-4 rad
D) 5.5 $\times$ 10^-8 rad
E) 3.7 $\times$ 10^-3 rad

Question 54

What is the limiting angle of resolution,in degrees,for a microscope with an objective 0.50 cm in diameter when viewing is done at 590 nm?

A) 2.1 $\times$ 10^-3
B) 4.1 $\times$ 10^-3
C) 7.2 $\times$ 10^-5
D) 8.2 $\times$ 10^-3
E) 1.4 $\times$ 10^-4

Question 55

When the slit width is doubled,what happens to the width of the central maximum in the diffraction pattern?

A) nothing
B) it doubles
C) it halves
D) it quadruples
E) it quarters

Question 56

Huygen's Principle only applies to

A) electromagnetic waves.
B) water waves.
C) sound waves.
D) all of these choices are correct

Question 57

A single slit of width 0.0300 mm is used to project a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit.What angle does the central maximum subtend as measured from the slit?

A) 1.91 $^{\circ}$
B) 3.82 $^{\circ}$
C) 0.945 $^{\circ}$
D) 1.50 $^{\circ}$
E) 3.00 $^{\circ}$

Question 58

How far away can two point sources of wavelength 500 nm be if they are just resolved in a telescope of aperture 1.5 cm?

A) 25 km
B) 12 km
C) 90 m
D) 12 m
E) more information is needed

Question 59

When light of wavelength 700 nm is used in a single-slit diffraction pattern,the central maximum has a width of 3.5 cm.When the light source is replaced by one of wavelength 500 nm,what central width will result?

A) 3.5 cm
B) 3.0 cm
C) 2.5 cm
D) 4.9 cm
E) 4.0 cm

Question 60

X-rays of wavelength 0.080 nm are used in a Bragg scattering experiment with a crystal.If the first order maximum is found at a grazing angle of 6.0 $^{\circ}$ ,what is the plane spacing in the crystal?

A) 0.31 nm
B) 0.71 nm
C) 1.4 nm
D) 0.38 nm
E) 0.77 nm

Question 61

Light from a HeNe laser (632.8 nm wavelength) is directed upon a human hair,in an attempt to measure its diameter by examining the diffraction pattern.The hair is mounted in a frame 7.5 m from a wall and the central diffraction maximum is measured to be 14.6 cm wide.What is the diameter of the hair?

A) 65 microns
B) 32.5 microns
C) 43.3 microns
D) 86.6 microns

Question 62

When scattering 3.28 Angstrom X-rays from a crystal an interference maximum occurs at a scattering angle of 23.0 degrees.What is the crystal spacing?

A) 4.2 Angstroms
B) 16.8 Angstroms
C) 6.3 Angstroms
D) 8.4 Angstroms

Question 63

Two planes of a crystal are separated by 3.25 Angstroms (or 3.25 $\times$ 10^-10 m). How many maxima will there be in the diffraction pattern of 2.0 Angstrom X-rays from this crystal?

A) 4
B) 2
C) 3
D) an infinite number
E) 1

Question 64

If the two slits in a two-slit apparatus kept the same width,but the distance between the two slits is increased,the number of interference fringes within the diffraction maximum will:

A) decrease
B) increase
C) may do any of the above.
D) remain the same

Question 65

When scattering 3.28 Angstrom X-rays off a crystal an interference maximum occurs at a scattering angle of 23.0 degrees.At what angle does the second maximum occur?

A) 51.3 $^{\circ}$
B) 46.0 $^{\circ}$
C) 34.5 $^{\circ}$
D) there is no second maximum.

Question 66

A holographic plate produces an image for the viewer that is:

A) real
B) virtual
C) may be either virtual or real

Question 67

Two planes of a crystal are separated by 3.25 Angstroms (or 3.25 $\times$ 10^-10 m). Light of what wavelength shows constructive interference at a scattering angle of 17.5 degrees?

A) 3.9 Angstroms
B) 0.49 Angstroms
C) 9.75 Angstroms
D) 1.46 Angstroms
E) 1.95 Angstroms

Question 68

A canvas tent has a single,tiny hole in its side.While inside the tent,you observe on the wall of the tent which is 2.0 m away from your eye a dot (due to the Sun's light incident upon the hole) of width 2.0 mm,with a faint ring around it.What is the size of the hole in the tent?

A) 0.76 mm
B) 1.24 mm
C) 0.31 mm
D) 0.62 mm

Question 69

In a two-slit experiment,there are 11 bright fringes within the central diffraction maximum.What is the ratio of the slit width to the slit separation?

A) 5
B) 1/6
C) 1/5
D) 6

Question 70

A single slit is opened in an opaque barrier.Light is shone through the slit and the diffraction pattern is observed.If the slit is decreased in size to half its original size,by what factor does the width of the central diffraction maximum change?

A) decreases by a factor four
B) Doubles
C) Halves
D) Increases four times

Question 71

A two-slit apparatus is covered with a red (660 nm) filter.When white light is shone on the filter,on the screen beyond the two-slit apparatus,there are 9 interference minima within the 4.5 cm-wide central diffraction maximum.When a blue (440 nm) filter replaces the red,how many fringes will there be in the central diffraction maximum?

A) 3
B) 13
C) 9
D) 6