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. It is partly reflected at the upper and the lower surfaces of the layer ant the two reflected rays interface . If `lambda = 648 nm`, obtain the least value of `t ("in" 10^(-8)m )` which the rays interface constructively.

Explanation

Path difference between rays reflected from upper and lower faces of layer ` = 2 mu t` (for narmal incidence)
Path difference due to reflection form denser (upper) surface. Is `lambda//2`.
condition of constructive interference (or maxima) is
`2 mu t + (lambda)/(2) = n lambda`
`t = (1)/(2 mu) (2 n - 1) (lambda)/(2) = ((2 n -1)lambda)/(4 mu) , n = 1, 2, 3,...`
For least thickness, `n = 1`.
`:. t_(min) = (lambda)/(4 mu) = (648)/(4 xx 1.8) nm = 90 nm`
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