27-16) A tank of gasoline (n = 1.40) is open to the air (n = 1.00). A thin film

Question

27-16) A tank of gasoline (n = 1.40) is open to the air (n = 1.00). A thin film of liquid floats on the gasoline and has a refractive index that is between 1.00 and 1.40. Light that has a wavelength of 646 nm (in vacuum) shines perpendicularly down through the air onto this film, and in this light the film looks bright due to constructive interference. The thickness of the film is 219 nm and is the minimum nonzero thickness for which constructive interference can occur. What is the refractive index of the film?

Explanation / Answer

You'll get constructive interference when the optical thickness of the film is a multiple of 1/2 wavelength (i.e., out and back through the film is some number of complete wavelengths). So, for the bright fringe with the longest wavelength, (264 nm)n = (606 nm/2) n = 303/264 ~ 1.15

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