Chapter 22

# Chapter 22 - Visualize The interference pattern looks like...

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22.1. 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 sin m dm λ = m = 0, 1, 2, 3, … () 9 2 6 2 500 10 m sin 0.02 50 10 m × ⇒= = × 2 0.020 rad = 180 0.020 rad 1.15 rad π ° = ×= °

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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 21 rrr Δ =− , where ( ) 2 2 500 nm 1000 nm rm λλ Δ= = = = 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). Solve: The bright fringes are located at positions given by Equation 22.4, sin . m dm θ λ = For the m = 3 bright orange fringe, the interference condition is ( ) 9 3 sin 3 600 10 m d . For the m = 4 bright fringe the condition is 4 sin 4 . d = Because the position of the fringes is the same, ( ) ( ) 99 3 34 4 sin sin 4 600 10 m 450 nm dd θθ −− == = ×⇒ = × =

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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 formula for fringe spacing is L y d λ Δ= () 39 1.8 10 m 600 10 m L d −− ×= × 3000 L d = The wavelength is now changed to 400 nm, and , L d being a part of the experimental setup, stays the same. Applying the above equation once again, 9 400 10 m 3000 1.2 mm L y d = × =
22.5. Visualize: The fringe spacing for a double slit pattern is . L y d λ Δ= We are given 20 m L =. and 600 nm. = We also see from the figure that 1 3 cm. y Δ = Solve: Solve the equation for d . 9 2 1 3 (600 10 m)(2 0 m) 036±mm 10 m L d y ×. == = . Δ× Assess: 0.36 mm is a typical slit spacing.

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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 fringe spacing is 92 3 (589 10 m)(150 10 m) 0.22 mm 4.0 10 m LL yd dy λ −− ×× Δ= ⇒ = = = Δ×
22.7. 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: () 1 2 m L ym d λ =+ m = 0, 1, 2, 3, … 11 51 22 L L yy dd ′′ −=+ −+ 2 3 3 4( 6 01 0 m ) 6.0 10 m 0.20 10 m × ×= × 500 nm =

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22.8. Model: Two closely spaced slits produce a double-slit interference pattern.
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## This note was uploaded on 01/30/2011 for the course PHYS 131 taught by Professor E.salik during the Winter '10 term at Cal Poly Pomona.

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Chapter 22 - Visualize The interference pattern looks like...

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