Find the minimum thickness of a film with refractive index `1.33` at which light with wavelength `0.64 mu m` experiences maximum reflection while light with wavelength `0.40 mu m` is not reflected at all. The incidence angle of light is equal to `30^(@)`.

Explanation

Given `2d sqrt(n^(2) - 1//4) = (k + (1)/(2)) xx 0.64 mu m` (bright fringe)
`2d sqrt(n^(2) - 1//4) = k xx 0.40 mu m`(dark fringe)
where `k, k'` are integers.
Thus `64(k + (1)/(2)) = 40 k'` or `4(2k + 1) = 5k'`
This means, for the smaller integer solutions
`k = 2, k' = 4`
Hence `d = (4 xx 0.40)/(2sqrt(n^(2) - 1//4)) = 0.65 mu m`.