Diffused monochromatic light with wavelength `lambda = 0.60 mu m` falls on a thin film with refractive index `n = .5`. Determine the film thickness if the angular separation of neighbouring maxima observed in reflected light at the amgles close to `theta = 45^(@)` to the normal is equal to `del theta = 3.0^(@)`.

Explanation

We have the condition for maxima
`2dsqrt(n^(2) - sin^(2) theta_(1)) = (k + (1)/(2)) lambda`
This must hold for angle `theta +- (del theta)/(2)` with successive values of `k`. Thus
`2d sqrt(n^(2) - sin^(2) (theta + (del theta)/(2))) = (k - (1)/(2)) lambda`
`2d sqrt(n^(2) - sin^(2) (theta - (del theta)/(2))) = (k + (1)/(2)) lambda`
Thus `lambda 2d {sqrt(n^(2) - sin^(2)theta + del theta sin theta cos theta) -sqrt(n^(2) - sin^(2) theta - del theta sin theta cos theta)}`
`= 2d (del theta sin theta cos theta)/(sqrt(n^(2) - sin^(2) theta))`
Thus `d = (sqrt(n^(2) - sin^(2) theta lambda))/(sin 2 theta del theta) =15.2 m um`