A puddle of water has a thin film of gasoline floating on it.A beam of light is shining perpendicular on the film.If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and water are 1.40 and 1.33,respectively,what is the minimum thickness of the film to see a bright reflection?
A) 100 nm
B) 200 nm
C) 300 nm
D) 400 nm
E) 500 nm

Question

Quizplus · Accepted Answer

For constructive interference, the path length difference between the reflected rays from the top and bottom surfaces of the film must be an integer multiple of the wavelength. The path length difference is 2nt, where n is the index of refraction of the film and t is its thickness. For a bright reflection, the path length difference must be an odd multiple of half the wavelength, or (2m+1)λ/2, where m is an integer. Substituting this into the equation 2nt = (2m+1)λ/2, we get t = (2m+1)λ/4n. For the minimum thickness, m = 0, so t = λ/4n. Substituting the given values, we get t = 560 nm / (4 * 1.40) = 100 nm.

A Puddle of Water Has a Thin Film of Gasoline