In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength `lambda`), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

Options

A. `2lambda`
B. `(2lambda)/(3)`
C. `(lambda)/(3)`
D. `lambda`

Answer

A

Explanation

Path difference due to slab should be integral multiple of `lambda` or `Delta x = n lambda`
or `(mu-1)t = n lambda, n =1,2,3 or t= (n lambda)/(mu-1)`
for minimum value of `t, n = 1`
`t = (lambda)/(mu - 1) = (lambda)/(1.5-1) = 2 lambda`