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Unformatted text preview: . . . . . . . . . . . . L 2 a L 2 b θ θ • T R • We use the identity sin 2 θ = tan 2 θ/ (1 + tan 2 θ ) to show that sin θ = ( a + x ) / p D 2 + ( a + x ) 2 . This means L 2 a = a sin θ = a p D 2 + ( a + x ) 2 a + x and L 2 b = x sin θ = x p D 2 + ( a + x ) 2 a + x . Therefore, L 2 = L 2 a + L 2 b = ( a + x ) p D 2 + ( a + x ) 2 a + x = p D 2 + ( a + x ) 2 . Using the binomial theorem, with D 2 large and a 2 + x 2 small, we approximate this expression: L 2 ≈ D +( a + x ) 2 / 2 D . The distance traveled by the direct wave is L 1 = p D 2 + ( a − x ) 2 . Using the binomial theorem, we approximate this expression: L 1 ≈ D + ( a − x ) 2 / 2 D . Thus, L 2 − L 1 ≈ D + a 2 + 2 ax + x 2 2 D − D − a 2 − 2 ax + x 2 2 D = 2 ax D . Setting this equal to ( m + 1 2 ) λ , where m is zero or a positive integer, we ±nd x = ( m + 1 2 )( D/ 2 a ) λ ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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