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Ch 22 Physics for Scientists and Engineers

# Ch 22 Physics for Scientists and Engineers - 22.1 Visualize...

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22.1. Visualize: Please refer to Figure Ex22.1. Solve: (a) (b) The initial light pattern is a double-slit interference pattern. It is centered behind the midpoint of the slits. The slight decrease in intensity going outward from the middle indicates that the light from each of the individual slits is not uniform but slowly decreases toward the edges of the screen. If the right slit is covered, light comes through only the left slit. Without a second slit, there is no interference. Instead, we get simply the spread-out pattern of light diffracting through a single slit, such as in the center of the photograph of Figure 22.2. The intensity is a maximum directly behind the left slit, and—as we discerned from the intensities in the double-slit pattern—the single-slit intensity fades gradually toward the edges of the screen.

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22.2. Model: Two closely spaced slits produce a double-slit interference pattern. Visualize: The interference pattern looks like the photograph .of Figure 22.3(b). It is symmetrical, with the m = 2 fringes on both sides of and equally distant from the central maximum. Solve: The two paths from the two slits to the m = 2 bright fringe differ by r r r = 2 1 , where r m = = = ( ) = λ λ 2 2 500 nm 1000 nm Thus, the position of the m = 2 bright fringe is 1000 nm farther away from the more distant slit than from the nearer slit.
22.3. Model: Two closely spaced slits produce a double-slit interference pattern. Visualize: The interference pattern looks like the photograph of Figure 22.3(b). It is symmetrical with the m = 2 fringes on both sides of and equally distant from the central maximum. Solve: The bright fringes occur at angles θ m such that d m m sin θ λ = m = 0, 1, 2, 3, … = × ( ) × ( ) = sin . θ 2 9 6 2 500 10 50 10 0 02 m m θ 2 = 0.020 rad = × ° = ° 0.020 rad rad 180 1 15 π .

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22.4. Model: Two closely spaced slits produce a double-slit interference pattern. Visualize: The interference pattern looks like the photograph of Figure 22.3(b). Solve: The fringe spacing is y L d d L y = = = × ( ) × ( ) × λ λ 589 10 150 10 4 0 10 9 2 3 m m m . = 0.221 mm
22.5. Model: Two closely spaced slits produce a double-slit interference pattern. Visualize: The interference pattern looks like the photograph of Figure 22.3(b). Solve: The dark fringes are located at positions given by Equation 22.9: ′ = + ( ) y m L d m 1 2 λ m = 0, 1, 2, 3, … ′ − ′ = + ( ) + ( ) y y L d L d 5 1 1 2 1 2 5 1 λ λ 6 0 10 4 60 10 0 20 10 3 2 3 . . × = × ( ) × m m m λ λ = 500 nm

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22.6. Model: Two closely spaced slits produce a double-slit interference pattern. Visualize: The interference pattern looks like the photograph of Figure 22.3(b). Solve: The formula for fringe spacing is y L d = λ 1 8 10 600 10 3 9 . × = × ( ) m m L d L d = 3000 The wavelength is now changed to 400 nm, and L d , being a part of the experimental setup, stays the same.
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