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

Answer

A

Explanation

Path difference due to slab should be an integral multiple of `lambda`.
i.e., `Delta x = (mu - 1) t = n lambda`
`t = (n lambda)/(mu - 1)`
For minimum value of `t, n = 1`
`t = (1 lambda)/(1.5 - 1) = 2 lambda`