Two waves of light in air, of wavelength lambda = 638.0 nm, are initially in pha

Question

Two waves of light in air, of wavelength lambda = 638.0 nm, are initially in phase. They then both travel through a layer of plastic as shown in the figure below, with L1 = 4.00 mu m, L2 = 3.50 mu m, n1 1.39, and n2 = 1.60. What multiple of lambda gives their phase difference after they both have emerged from the layers? If the waves later arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive, or intermediate but closer to fully destructive? fully constructive fully destructive intermediate but closer to fully constructive intermediate but closer to fully destructive

Explanation / Answer

A. In general multiple of wavelength:

N = Ln/lambda

lambda = 638 nm = 0.638 um

N2 = L2*n2/lambda + (L1 - L2)*1/lambda

N2 = 3.50*1.6/0.638 + (4.0 - 3.50)*1/0.638 = 9.561

N1 = L1*n1/lambda = 4*1.39/0.638 = 8.714

phase difference = N2 - N1 = 9.561 - 8.714 = 0.847

B. 0.847 is closer to full integer (eg. 1) than half integer, so interfernce is more constructive than destructive.

Ans is option C

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