# Problem: Thin-film interference is responsible for the fact that certain birds and inspects can appear different colors. Consider a very thin layer of oil (n=1.30) stretched the wisps of a bird feather, so that it has air on either side. Assume that the oil layer has uniform thickness t.When you look at the feather with normal incidence, it strongly reflects green light of wavelength 500 nm. What is the minimum possible thickness of the oil layer?

###### FREE Expert Solution

Constructive interference condition:
$\overline{){\mathbf{2}}{\mathbf{\eta tc}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}{\mathbf{=}}{\mathbf{\left(}}{\mathbf{m}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\right)}}{\mathbf{\lambda }}}$

Both sides of the film have a rare medium.

Such a case allows for 180° phase shift whenever the light waves strike a denser medium.

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###### Problem Details

Thin-film interference is responsible for the fact that certain birds and inspects can appear different colors. Consider a very thin layer of oil (n=1.30) stretched the wisps of a bird feather, so that it has air on either side. Assume that the oil layer has uniform thickness t.

When you look at the feather with normal incidence, it strongly reflects green light of wavelength 500 nm. What is the minimum possible thickness of the oil layer?