Question

A thin film of gasoline floats on a puddle of water at a gas station. Sunlight falls on the film and reflects to your eyes. You see yellow because blue (wavelength 469 nm in vacuum) undergoes destructive interference. The index of refraction for gas is 1.40 and for water is 1.33. (a) What is the wavelength of the blue light inside the gasoline? (b) What is the minimum thickness of the film?

Answer 1

part a )

lambda_film = lambda_vacuum/n

n = 1.4

lambda_vaccum = 4.69 x 10^-7 m

lambda_film = 3.35 x 10^-7 m

part b )

When light travels through a material with a smaller refractive index towards a material with a larger refractive index, reflection at the boundary occurs along with a phase change that is equivalent to one-half of a wavelength in the film. When light travels from a larger towards a smaller refractive index, there is no phase change upon reflection

2t + lambda_film/2 = (m+1/2)*lambda_film

minimum thickness m = 1

t = 1*lambda_film/2

t = 1.675 x 10^-7 m = 167.5 nm