A film of oil on water will appear dark when it is very thin, because the path l

Question

A film of oil on water will appear dark when it is very thin, because the path length difference for reflected light becomes small compared to the wavelength of the light and there is a phase shift upon reflection at the outer surface. In this problem, assume the wavelength of visible light is in the range 400 nm to 700 nm.

a. If the oil film becomes dark when the path length difference is less than one fourth the wavelength, what is the thickest the oil film can be and appear dark at all visible wavelengths? Give your answer in nanometers, and assume that oil has an index of refraction of 1.40.

Explanation / Answer

Note that

OPD = 2 n t < (1/4)wavelength

where t is the thickness of the film.

As the minimum visible wavelength is around 390 nm, then

2 (1.40) t < (1/4)(390 nm)

Thus,

t < 34.8 nm

Thus, thickest oil film to satisfy the condition is 34.8 nm. [ANSWER]

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