951_PartUniversity Physics Solution

951_PartUniversity Physics Solution - The Nature and...

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The Nature and Propagation of Light 33-9 33.34. IDENTIFY: Use the transmitted intensity when all three polairzers are present to solve for the incident intensity 0 I . Then repeat the calculation with only the first and third polarizers. SET UP: For unpolarized light incident on a filter, 1 0 2 II = and the light is linearly polarized along the filter axis. For polarized light incident on a filter, 2 max (cos ) φ = , where max I is the intensity of the incident light, and the emerging light is linearly polarized along the filter axis. EXECUTE: With all three polarizers, if the incident intensity is 0 I the transmitted intensity is 22 1 00 2 ( )(cos23.0 ) (cos[62.0 23.0 ]) 0.256 I =− = °° ° . 2 2 0 75.0 W/cm 293 W/cm 0.256 0.256 I I == = . With only the first and third polarizers, 2 1 2 ( )(cos62.0 ) 0.110 (0.110)(293 W/cm ) 32.2 W/cm I = = ° . EVALUATE: The transmitted intensity is greater when all three filters are present. 33.35. IDENTIFY: The shorter the wavelength of light, the more it is scattered. The intensity is inversely proportional to the fourth power of the wavelength. SET UP: The intensity of the scattered light is proportional to 1/ λ 4 , we can write it as I = (constant)/ 4 . EXECUTE: (a) Since I is proportional to 1/ 4 , we have I = (constant)/ 4 . Taking the ratio of the intensity of the red light to that of the green light gives 4 4 4 RR G 4 GR (constant)/ 520 nm (constant)/ 665 nm I I λλ ⎛⎞ = ⎜⎟ ⎝⎠ = 0.374, so I R = 0.374 I. (b) Following the same procedure as in part (a) gives 4 4 VG V 520 nm 420 nm I I = 2.35, so I V = 2.35 I. EVALUATE: In the scattered light, the intensity of the short-wavelength violet light is about 7 times as great as that of the red light, so this scattered light will have a blue-violet color. 33.36. IDENTIFY: As the wave front reaches the sharp object, every point on the front will act as a source of secondary wavelets. SET UP: Consider a wave front that is just about to go past the corner. Follow it along and draw the successive wave fronts. EXECUTE: The path of the wavefront is drawn in Figure 33.36. EVALUATE: The wave fronts clearly bend around the sharp point, just as water waves bend around a rock and light waves bend around the edge of a slit. Figure 33.36 33.37. IDENTIFY: Reflection reverses the sign of the component of light velocity perpendicular to the reflecting surface but leaves the other components unchanged. SET UP: Consider three mirrors, M 1 in the ( x,y )-plane, M 2 in the ( y,z )-plane, and M 3 in the ( x,z )-plane. EXECUTE: A light ray reflecting from M 1 changes the sign of the z -component of the velocity, reflecting from M 2 changes the x -component, and from M 3 changes the y -component. Thus the velocity, and hence also the path, of the light beam flips by 180 ° EVALUATE: Example 33.3 discusses some uses of corner reflectors.
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This note was uploaded on 07/16/2011 for the course PHY 2053 taught by Professor Buchler during the Spring '06 term at University of Florida.

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951_PartUniversity Physics Solution - The Nature and...

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