A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of source can be varied continuously. The destructive interference 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. (a) `6.738xx10^-5cm`
B. (b) `5.7xx10^-5cm`
C. (c) `4xx10^-5cm`
D. (d) `2.8xx10^-5cm`

Answer

A

Explanation

In this case, both the rays suffer a phase change of `180^@` and the condition for destructive interference is: `2^(nd)=(m+1/2)lambda_1`
`2^(nd)=(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)=(2.5xx7000)/(2xx1.3)`
`=6738Å=6.738xx10^-5cm`.