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Exam 25: Interference and Diffraction

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Question 21

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Light of wavelength 450 nm produces a first-order maximum at 27° 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°
B) 40°
C) 36°
D) 37°
E) 14°

F) All of the above
G) A) and D)

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Question 22

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A general condition for two coherent waves to undergo destructive interference is that

A) their phase difference is zero.
B) their phase difference is π/2 rad.
C) their phase difference is ±π/2 rad.
D) their phase difference is an even integral multiple of π rad.
E) their phase difference is an odd integral multiple of π rad.

F) A) and D)
G) A) and E)

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Question 23

Multiple Choice

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A single slit of width 0.030 mm is used to produce 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?

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

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

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 third-order minima is 6.0 cm, what is the slit width?

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

What kind of image does a holographic plate produce for the viewer?

Holography was invented by

Light from a HeNe laser (632.8 nm wavelength) is directed upon a straightened strand of human hair, 7.5 m from the wall. By examining the diffraction pattern produced on the wall, the diameter of the hair can be determined (the diffraction pattern thus produced has minima in the same locations as if the hair were a slit of the same width in an otherwise opaque barrier) . If the central diffraction maximum is measured to be 14.6 cm wide, what is the diameter of the hair?

A two-slit apparatus is illuminated with red light of wavelength 660 nm, and 9 interference maxima are observed within the 4.5 cm-wide central diffraction maximum on a distant screen. If blue light of wavelength 440 nm is used instead, how many fringes will there be in the new central diffraction maximum?

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

A thin film of magnesium fluoride (n = 1.38) is applied to glass (n = 1.50) . If the thickness of the film is 100 nm, for what visible wavelength will it be nonreflecting?

A Michelson interferometer is used to measure the index of refraction of a gas by counting interference fringes as the gas is slowly leaked into a transparent vessel placed in one arm of the interferometer. The vessel initially contains a vacuum, and as the gas is let in, 397 bright fringes are counted. That is, the central region of the screen changes from bright to dark and back to bright 397 times. If the wavelength of light used is 560 nm, and the vessel containing the gas is 25.0 cm long, what is the index of refraction of the gas?

When scattering 0.328 nm x-rays off a crystal, the first interference maximum occurs at an angle of 23.0 degrees relative to the crystal surface. At what angle does the second maximum occur?

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 laser beam passes through a grating and produces a first-order maximum at an angle of 25°. At what angle is the second-order maximum?

When the slit width is doubled, what happens to the width of the central maximum in a single-slit diffraction pattern? Assume small angles.

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

Max von Laue is known for his work with