A plane wave of monochromatic light falls normally on a uniform thin or oil which covers a glass plate. The wavelength of source can be varied continuously. Complete destructive is observed for `lambda = 5000 Å` and `lambda = 1000 Å` and for no other wavelength in between. If `mu` of oil is 1.3 and that of glass is 1.5, the thickness of the film will be

Options

A. `6.738 xx 10(-5) cm`
B. `5.7 xx 10^(-5) cm`
C. `4 xx 10^(-5) cm`
D. `2.8 xx 10^(-5) cm`

Answer

a

Explanation

In this case, both the rays suffer a phase change of `180^(@)` and the conditions for destructive interference is
`2 n d = (m + (1)/(2)) lambda_(1)`
`2 n d = (m + (3)/(2)) lambda_(2)`
`:. (m + (1)/(2))/(m + (3)/(2)) = (lambda_(2))/(lambda_(1)) = (5000)/(7000) = (5)/(7)`
and `d = ((m + (1)/(2))lambda_(1))/(2n) = (2.5 xx 7000)/(2 xx 1.3)`
`= 6738 Å = 6.738 xx 10^(-5)cm`