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Unformatted text preview: 1383 Chapter 36 1. (a) We use Eq. 36-3 to calculate the separation between the first ( m 1 = 1) and fifth 2 ( 5) m minima: 2 1 sin . m D D y D D m m m a a a Solving for the slit width, we obtain a D m m y 2 1 6 400 550 10 5 1 0 35 2 5 b g b gc hb g mm mm mm mm . . . (b) For m = 1, sin . . . m a 1 550 10 2 5 2 2 10 6 4 bgc h mm mm The angle is = sin –1 (2.2 10 –4 ) = 2.2 10 –4 rad. 2. From Eq. 36-3, a l m sin 1 sin30.0 2.00. 3. (a) A plane wave is incident on the lens so it is brought to focus in the focal plane of the lens, a distance of 70 cm from the lens. (b) Waves leaving the lens at an angle to the forward direction interfere to produce an intensity minimum if a sin = m , where a is the slit width, is the wavelength, and m is an integer. The distance on the screen from the center of the pattern to the minimum is given by y = D tan , where D is the distance from the lens to the screen. For the conditions of this problem, sin . . . m a 1 590 10 0 40 10 1475 10 9 3 3 bgc h m m This means = 1.475 10 –3 rad and y = (0.70 m) tan(1.475 10 –3 rad) = 1.0 10 –3 m. 4. (a) Equations 36-3 and 36-12 imply smaller angles for diffraction for smaller wavelengths. This suggests that diffraction effects in general would decrease. CHAPTER 36 1384 (b) Using Eq. 36-3 with m = 1 and solving for 2 (the angular width of the central diffraction maximum), we find 2 2sin 1 l a 2sin 1 0.50m 6.0m 9.6 . (c) A similar calculation yields 0.23° for = 0.010 m. 5. (a) The condition for a minimum in a single-slit diffraction pattern is given by a sin = m , where a is the slit width, is the wavelength, and m is an integer. For = a and m = 1, the angle is the same as for = b and m = 2. Thus, a = 2 b = 2(350 nm) = 700 nm. (b) Let m a be the integer associated with a minimum in the pattern produced by light with wavelength a , and let m b be the integer associated with a minimum in the pattern produced by light with wavelength b . A minimum in one pattern coincides with a minimum in the other if they occur at the same angle. This means m a a = m b b . Since a = 2 b , the minima coincide if 2 m a = m b . Consequently, every other minimum of the b pattern coincides with a minimum of the a pattern. With m a = 2, we have m b = 4. (c) With m a = 3, we have m b = 6....
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This document was uploaded on 04/22/2011.
- Spring '11