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?
Refractive index = 1.40
Incident wavelength = 546.1 * 10-9 m
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