p36_007 - phase dierence is 1 2 = (2 / air )( n 1 n 2 ) L ....

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7. (a) We take the phases of both waves to be zero at the front surfaces of the layers. The phase of the Frst wave at the back surface of the glass is given by φ 1 = k 1 L ωt ,whe re k 1 (= 2 π/λ 1 )isthe angular wave number and λ 1 is the wavelength in glass. Similarly, the phase of the second wave at the back surface of the plastic is given by φ 2 = k 2 L ωt ,where k 2 (= 2 π/λ 2 ) is the angular wave number and λ 2 is the wavelength in plastic. The angular frequencies are the same since the waves have the same wavelength in air and the frequency of a wave does not change when the wave enters another medium. The phase di±erence is φ 1 φ 2 =( k 1 k 2 ) L =2 π µ 1 λ 1 1 λ 2 L. Now, λ 1 = λ air /n 1 ,where λ air is the wavelength in air and n 1 is the index of refraction of the glass. Similarly, λ 2 = λ air /n 2 ,whe re n
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Unformatted text preview: phase dierence is 1 2 = (2 / air )( n 1 n 2 ) L . The value of L that makes this 5 . 65 rad is L = ( 1 2 ) air 2 ( n 1 n 2 ) = 5 . 65(400 10 9 m) 2 (1 . 60 1 . 50) = 3 . 60 10 6 m . (b) 5 . 65 rad is less than 2 rad = 6 . 28 rad, the phase dierence for completely constructive interference, and greater than rad (= 3 . 14 rad), the phase dierence for completely destructive interference. The interference is, therefore, intermediate, neither completely constructive nor completely destructive. It is, however, closer to completely constructive than to completely destructive....
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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.

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