Practice Test IV. 3) Two coherent waves, each with intensity I 0, reach the same point in phase. The amplitude of the superposed wave is.

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1 Practice Test IV 1) A general condition that two waves undergo constructive 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. 2) 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 3) Two coherent waves, each with intensity I 0, reach the same point in phase. The amplitude of the superposed wave is. a) 0 b) I 0 c) 2 I 0 d) 3 I 0 e) 4 I 0 Ans: e 4) Two coherent waves reach the same point in phase. One wave has an intensity of 8.0 units and the other has an intensity of 4.0 units. What is the intensity of the superposed wave? a) 4.0 units b) 8.0 units c) 12.0 units d) 23.3 units e) 24.0 units 5) Wave 1 has intensity 9.0 units while wave 2 has intensity 4.0 units. What is their ratio of amplitudes, A 1 /A 2? a) 20 b) 5.1 c) 2.3 d) 1.5 e) 1.3

2 6) 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 7) 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 nm d) 80 nm e) 78 nm Ans: b 8) 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 x 10-3 cm b) 3.98 x 10-3 m c) 9.98 x 10-5 m d) 1.40 x 10-3 m e) 1.48 x 10-4 m Ans: e 9) If light of wavelength 690 nm is used in a double-slit experiment with slit separation mm, what angle separates the two 4 th order maxima? a) o b) 3.07 o c) o d) 1.54 o e) o 10) 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.

3 11) 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 Ans: a 12) What slit separation would a grating have to produce a first-order maximum at an angle of 40.0 o for a wavelength of 589 nm? a) 1090 nm b) 690 nm c) 378 nm d) 458 nm e) 916 nm Ans: e 13) A laser beam is shown through a grating and the first-order maximum is produced at 17 o. What is the highest order maximum that can be produced by this arrangement? a) 2 b) 3 c) 4 d) 5 e) 6 Ans: b 14) 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 Ans: b 15) A single slit of width 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 o b) 3.82 o c) o d) 1.50 o e) 3.00 o Ans: a

4 16) 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. 17) 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 18) In a single slit diffraction experiment, the width of the slit is m and the distance from the slit to the screen is 2.2 m. If the beam of light of wavelength 600 nm passes through the slit and forms a diffraction pattern on the screen, what is the linear distance on the screen from the center of the diffraction pattern to the first dark fringe? A) 2.1 cm B) 4.3 cm C) 6.3 cm D) 8.5 cm Answer: B 19) In a single-slit diffraction experiment, a beam of monochromatic light of wavelength 640 nm is incident on a slit of width mm. If the distance between the slit and the screen is 1.80 m, what are the positions of the first dark fringes? A) m B) m C) m D) m Answer: D 20) In a single-slit diffraction experiment, the width of the slit through which light passes is reduced. What happens to the central bright fringe? A) It stays the same. B) It becomes narrower. C) It becomes wider. D) None of the other answers is correct. Answer: C

5 21) 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. Answer: B 22) 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) red light. D) The separation is the same for all wavelengths. Answer: C 23) Helium-neon laser light (λ= m) is sent through a 0.30 mm-wide single slit. What is the width of the central maximum on a screen 1.0 m from the slit? a. 2.0 cm b. 4.2 mm c. 1.1 cm d. 2.0 mm e mm Answer: b 24) Monochromatic light from a He-Ne laser (λ = nm) is incident on a diffraction grating containing 5000 lines/cm. Determine the angle of the first-order maximum. a b c d e Answer: a 25) White light is spread out into spectral hues by a diffraction grating. If the grating has 1000 lines per cm, at what angle will red light (λ = 640 nm) appear in first order? a b c d e. 1.84

6 Answer: d 26) When you look at a single slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the wavelength of the light is increased, a. the pattern shrinks in size. (central maximum less wide; other maxima in closer to it) b. the pattern increases in size. (central maximum wider; other maxima farther from it) c. it does not affect the size of the pattern. d. the width of the central maximum increases, but the other maxima do not change in position or width. e. the width of the central maximum decreases, but the other maxima do not change in position or width. Answer: B