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Exam 22: Wave Optics

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Question 21

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Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32.0° from the central spot, how many TOTAL number of maxima can be seen?

A) 5
B) 7
C) 10
D) 11
E) 13

F) A) and E)
G) B) and E)

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Question 22

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Coherent monochromatic light of wavelength 632.8 nm passes through a pair of thin parallel slits. The figure shows the central portion of the pattern of bright fringes viewed on a screen 1.40 m beyond the slits. What is the distance between the two slits?

A) 0.0703 mm
B) 0.141 mm
C) 0.281 mm
D) 0.562 mm
E) 0.633 mm

F) None of the above
G) A) and C)

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Question 23

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A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the screen is 1.00 cm wide, as measured between the dark fringes that border it on either side. Which of the following actions would decrease the width of the central bright fringe? (There may be more than one correct choice.)

A He-Ne laser, which produces light of wavelength 632.8 nm, is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5° from the central spot, what is the distance between the slits of the grating?

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

In the figure, a slit 0.30 mm wide is illuminated by light of wavelength 426 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 diffraction minima on either side of the central diffraction maximum?

A single slit illuminated with a 500 nm light gives a diffraction pattern on a far screen. The 5^th minimum occurs at 7.00° away from the central maximum. At what angle does the 18^th minimum occur?

A slit of width 0.010 mm has light of frequency 5.0 × 10¹⁴ Hz passing through it onto a screen 60 cm away. How wide is the central maximum? (c = 3.00 × 10⁸ m/s)

Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A woman is standing opposite the midpoint between the speakers and is initially 35.0 m from the midpoint. As she slowly walks parallel to the line connecting the speakers, at what angle θ (relative to the centerline coming outward from the midpoint between the speakers) will she first hear no sound?

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, and a fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 complete bright fringes per centimeter on the screen near the center of the pattern, what is the wavelength of the monochromatic light?

What is the angular separation of the two second-order spectral lines having wavelengths 417 nm and 388 nm using a diffraction grating having 456 lines/mm?

A single slit, which is 0.050 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?

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 laser beam passes through a thin slit. When the pattern is viewed on a screen 1.25 m past the slit, you observe that the fifth-order dark fringes occur at ±2.41 cm from the central bright fringe. The entire experiment is now performed within a liquid, and you observe that each of the fifth-order dark fringes is 0.790 cm closer to the central fringe than it was in air. What is the index of refraction of this liquid?

An 18-mm wide diffraction grating has rulings of 880 lines per mm. Monochromatic light of 590 nm wavelength is incident normally on the grating. What is the largest angle, measured from the central bright spot, at which an intensity maximum is formed?

In the two-slit experiment, monochromatic light of frequency 5.00 × 10¹⁴ Hz passes through a pair of slits separated by 2.20 × 10^-5 m. (c = 3.00 × 10⁸ m/s) (a) At what angle away from the central bright spot does the third bright fringe past the central bright spot occur? (b) At what angle does the second dark fringe occur?

Monochromatic laser light of frequency 5.20 × 10¹⁴ Hz is shown on a pair of thin parallel slits, and the pattern is viewed on a screen 1.20 m away. The fifth bright fringes (not counting the central fringe) occur at ±2.12 cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent liquid. When the experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central bright fringe. (c = 3.00 × 10⁸ m/s) (a) How far apart are the slits? (b) What is the index of refraction of the liquid?

A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot. What is the TOTAL number of bright fringes that will show up on the screen?

In a double slit experiment, the slit separation is constructed to be exactly 4 times the wavelength of the light passing through the slits. At what angles from the center of the pattern will the third bright fringes on both sides of the central fringe occur?

In a two-slit experiment, the slit separation is 3.00 × 10^-5 m. The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits. If the seventh bright fringe on the detector is 10.0 cm away from the central fringe, what is the wavelength of the light passing through the slits?