Student Name: Problems for CH *Chapter 36, Problem 7 GO. 2. *Chapter 36, Problem *Chapter 36, Problem *Chapter 36, Problem 39

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1 1 of 5 5/21/2009 6:55 PM Student Name: Problems for CH36 1. *Chapter 36, Problem 7 GO The distance between the first and fifth minima of a single-slit diffraction pattern is mm with the screen 43.0 cm away from the slit, when light of wavelength 570 nm is used. Find the slit width. 2. *Chapter 36, Problem 11 Monochromatic light with wavelength 667 nm is incident on a slit with width mm. The distance from the slit to a screen is 3.3 m. Consider a point on the screen 1.1 cm from the central maximum. Calculate (a)θ for that point, (b) α, and (c) the ratio of the intensity at that point to the intensity at the central maximum. (a) (b) (c) Answer c1: significant digits are disabled; the tolerance is +/-4% 3. *Chapter 36, Problem 23 Find the separation of two points on the Moon's surface in meters that can just be resolved by a telescope with a mirror diameter of 5.6 m, assuming that this separation is determined by diffraction effects. The distance from Earth to the Moon is 3.82 x 10 5 km. Assume a wavelength of 550 nm. 4. *Chapter 36, Problem 39 (a) How many fringes appear between the first diffraction-envelope minima to either side of the central maximum in a double-slit pattern if λ = 696 nm, d = mm, and a = 23.1 µm? (b) What is the ratio of the intensity of the third bright fringe to the intensity of the central fringe? (a) (b)

2 2 of 5 5/21/2009 6:55 PM 5. *Chapter 36, Problem 46 Perhaps to confuse a predator, some tropical gyrinid beetles (whirligig beetles) are colored by optical interference that is due to scales whose alignment forms a diffraction grating (which scatters light instead of transmitting it). When the incident light rays are perpendicular to the grating, the angle between the first-order maxima (on opposite sides of the zeroth-order maximum) is about 26 in light with a wavelength of 558 nm. What is the grating spacing of the beetle? 6. *Chapter 36, Problem 54 GO A beam of light consisting of wavelengths from 470 nm to 630 nm is directed perpendicularly onto a diffraction grating with 140 lines/mm. (a) What is the lowest order that is overlapped by another order? (b) In the highest complete order, at what angle does the light of wavelength 630 nm appear? (a) (b) Answer a1: significant digits not applicable; exact number, no tolerance 7. *Chapter 36, Problem 61 A source containing a mixture of hydrogen and deuterium atoms emits light at two wavelengths whose mean is nm and whose separation is nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order. 8. *Chapter 36, Problem 67 X rays of wavelength 0.14 nm are found to undergo second-order reflection at a Bragg angle of 21 from a crystal. What is the interplanar spacing of the reflecting planes in the crystal?

3 3 of 5 5/21/2009 6:55 PM 9. Test Bank, Question 10 In the equation = (2 a/ ) sin for single-slit diffraction, is: the angle to the first minimum the angle to the second maximum the phase angle between the extreme rays N where N is an integer (N + 1/2) where N is an integer 10. Test Bank, Question 20 A diffraction pattern is produced on a viewing screen by illuminating a long narrow slit with light of wavelength. If is increased and no other changes are made: neither the intensity at the center of the pattern nor the pattern itself change the intensity at the center of the pattern decreases and the pattern expands away from the bright center the intensity at the center of the pattern does not change and the pattern expands away from the bright center the intensity at the center of the pattern does not change and the pattern contracts toward the bright center the intensity at the center of the pattern increases and the pattern contracts toward the bright center 11. Test Bank, Question 30 Two stars that are close together are photographed through a telescope. The black and white film is equally sensitive to all colors. Which situation would result in the most clearly separated images of the stars? Small lens, red stars Small lens, blue stars Large lens, red stars Large lens, blue stars

4 4 of 5 5/21/2009 6:55 PM Large lens, one star red and the other blue 12. Test Bank, Question 40 An N-slit system has slit separation d and slit width a. Plane waves with intensity I and wavelength are incident normally on it. The angular separation of the lines depends only on: a and N a and N and d and I and N 13. *Chapter 36, Problem 20 Assume that Rayleigh's criterion gives the limit of resolution of an astronaut's eye looking down on Earth's surface from a typical space shuttle altitude of 415 km. (a) Under that idealized assumption, estimate the smallest linear width on Earth's surface that the astronaut can resolve. Take the astronaut's pupil diameter to be 4 mm and the wavelength of visible light to be 560 nm. (b) Can the astronaut resolve the Great Wall of China (figure 36-43), which is more than 3000 km long, 5 to 10 m thick at its base, 4 m thick at its top, and 8 m in height (1 depicts "yes", 0 otherwise)? (c) Would the astronaut be able to resolve any unmistakable sign of intelligent life on Earth's surface (1 depicts "yes", 0 otherwise)? (a)

5 5 of 5 5/21/2009 6:55 PM (b) (c) Answer b1: significant digits not applicable; exact number, no tolerance Answer c1: significant digits not applicable; exact number, no tolerance