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

Question

A tank of gasoline (n = 1.40) is open to the air (n = 1.00). A thin film of some other liquid floats atop
the gasoline. This floating liquid has an index of refraction greater than 1.00 but less than 1.40. The
floating layer is 242 nm thick. Light traveling through the air with a wavelength of 625 nm is incident
perpendicularly onto this film, and as a result the film looks very bright in this color to an observer
looking down onto the film from above. Assuming that the film is the minimum thickness for which this
could occur, what is the index of refraction of this floating liquid?

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,
(242 nm)n = (625 nm/2)
n = 625/(2*242) ~ 1.29

n ~ 1.29

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