A soap film has an index of refraction n = 1.62. The film is viewed in transmitt

Question

A soap film has an index of refraction n = 1.62. The film is viewed in transmitted light. (a) At a spot where the film thickness is 966.0 nm, which wavelengths are missing in the transmitted light? (Enter your answers in order, least to greatest, from left to right. If there are more than 3 such visible wavelengths, enter the 3 smallest.)

(b) Which wavelengths are strongest in transmitted light? (Enter your answers in order, least to greatest, from left to right. If there are more than 3 such visible wavelengths, enter the 3 smallest.)

Explanation / Answer

For transmission, we're looking at differences between beams that pass through the film once and those that pass three times with two internal reflections. The internal-reflection phase shifts are the same (0), so for A (cancellation) the additional 2T path-length is a phase shift = odd-integer*1/2*lambda/n, and for B (reinforcement) 2T = integer*lambda/n.
Since the question is about visible wavelengths, we look for lambda = 380 to 770 nm.
A. 2T = odd-integer*1/2*lambda/n
lambda = 4nT/odd-integer =

= 4*1.62*966(1,3,5.......) =

= 894.24, 695.52, 569.06 nm for odd integar 7,9, 11

B. 2T = integer*lambda/n
lambda = 2nT/integer = 2*1.62*966(1,2,3,........)

= 782.46, 625.968, 521.64 nm for integar 4,5,6

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