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Problem 4: A soap film has a refractive index of 1.40. How thick must the film be if it appears black when mercury light of wavelength 546.1 nm falls on it normally?

Solution

Given data

Refractive index = 1.40                 

Incident wavelength = 546.1 * 10-9 m

Required

Thickness of the film = x =?

Theory                            Since the reflected beam of light from the inner surface passes the soap film thickness twice, therefore, the path difference = 2x     …     (1)

Now for the soap film we have,

Compare equations (1) and (2)

For first order fringe, m =1

Put values in the above formula

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