1061_Physics ProblemsTechnical Physics

1061_Physics ProblemsTechnical Physics - 402 P37.60...

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402 Interference of Light Waves P37.60 Bright fringes occur when 2 1 2 t n m =+ F H G I K J λ and dark fringes occur when 2 t n m = F H G I K J . The thickness of the film at x is t h x = F H G I K J A . Therefore, x hn m bright F H G I K J A 2 1 2 and x m hn dark = A 2 . FIG. P37.60 P37.61 Call t the thickness of the film. The central maximum corresponds to zero phase difference. Thus, the added distance r traveled by the light from the lower slit must introduce a phase difference equal to that introduced by the plastic film. The phase difference φ is φπ = F H G I K J 21 t n a af . The corresponding difference in path length r is r t nt n a a a = F H G I K J = F H G I K J F H G I K J =− π 2 2 1 . Screen θ y' Zero order m = 0 L Thin film α r d FIG. P37.61 Note that the wavelength of the light does not appear in this equation. In the figure, the two rays from the slits are essentially parallel. Thus the angle may be expressed as tan == r d y L . Eliminating r by substitution, = y L tn d 1 gives
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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