HW03solutions - 22.2 Model Two closely spaced slits produce...

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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 2 1 r r r Δ = , where ( ) 2 2 500 nm 1000 nm r m λ λ 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.
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22.10. Model: A diffraction grating produces a series of constructive-interference fringes at values of m θ determined by Equation 22.15. Solve: We have sin 0, 1, 2, 3, m d m m θ λ = = sin 20.0 1 d λ ° = and 2 sin 2 d θ λ = Dividing these two equations, 2 sin 2sin20.0 0.6840 θ = ° = 2 43.2 θ = °
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22.14. Model: Assume the screen is centered behind the slit. We actually want to solve for m , but given the other data, it is unlikely that we will get an integer from the equations for the edge of the screen, so we will have to truncate our answer to get the largest order fringe on the screen. Visualize: Refer to Figure 22.7. Use Equation 22.15: sin , m d m θ λ = and Equation 22.16: tan . m m y L θ = We are given 510 nm, λ = 2 0 m, L = . and 1 500 mm. d = As mentioned above, we are not guaranteed that a bright fringe will occur exactly at the edge of the screen, but we will kind of assume that one does and set 1 0 m; m y = . if we do not get an integer for m then the fringe was not quite at the edge of the screen and we will truncate our answer to get an integer m . Solve: Solve Equation 22.16 for m θ and insert it in Equation 22.15.
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