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.

Options

A. `30 nm`
B. `60 nm`
C. `90 nm`
D. `120 nm`

Answer

C

Explanation

Conducting for constructive refrence
`2mu t= (2n-1)(lambda)/(2) [n = 1,2,3,- - -] t = (2n-1) (lambda)/(4mu)`
For least value of 't' , `n = 1 t_("min") = [2(1) - 1] (lambda)/(4mu)`
`mu = 1.8 }t`
`mu = 1.5`
`t_(min) = (lambda)/(4mu) = (648xx10^(-9))/(4xx1.8)`
`t_(min) = 90xx10^(-9)m t_(min) = 90nm`