= Thin-film interference
{wiki}
<Thin-film interference> combines coherent <light> contributions reflected or transmitted at the two surfaces of a layer. For a film of <refractive index> $n$, thickness $d$ and internal angle $\theta_t$, the round-trip <optical path difference> is $2nd\cos\theta_t$. The relative reflection <phase shift> must also be included. For a nonabsorbing higher-index film surrounded by air, one of the two leading reflected contributions has a $\pi$ <phase shift> and the other does not. Reflection maxima therefore satisfy $2nd\cos\theta_t=(m+1/2)\lambda_0$. A smooth reflection spectrum filters many visible <wavelengths> at once; varying thickness and angle produce spatially varying mixed colours.
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