A glass of refractive index `1.5` is coated with a thin layer of thickness t and refractive index `1.8` Light of wavelength `lambda` travelling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and two reflected rays interfere. Write the condition for their constructive interfere. If the `lambda = 648nm`, obtain the least value of t for which the rays interfere constrcutively.

Answer

a

Explanation

Path difference between rays reflected from upper and lower faces of layer `= 2 mu t cos r = 2 mu t` (for normal incidence.) But there is abrupt change in path of `lambda // 2` of light at upper surface. So actual path difference is `2mu t - lambda // 2`
For constructive interference `2 mu t - (lambda)/(2) = n lambda`
`t = ((2n + 1 )lambda)/(4 mu)`. For least thickness `n = 0`
`:. t_(min) = (lambda)/(mu - 1) = (648)/(4 xx 1.8) nm = 90 nm`