A glass plate of thickness d and refractiv index n is placed on the path of one of the twi coming out of two slits in Young's experiment The minimum thickness of plate for havin zero intensity of central bright fringe should be ........`lambda` is the wavelength of light

Options

A. `(n-1)(lambda)/(2)`
B. `(lambda)/(n-1)`
C. `(lambda)/(2(n-1))`
D. `(n-1) lambda`

Answer

C

Explanation

In Young.s experiment path difference is (n-1) of a glass of refractive index .n. of thickness .d. in its path of ray coming out from a slit If the intensity is zero than it is dark
For dark fringe of `m^(th)` number,
Path minimum thickness of plate m=1
`:. (n-1)d=(2m-1)(lambda)/(2)`
For minimum thickness of plane m=1
`:. (n-1)d=(lambda)/(2)`
`:. d=(lambda)/(2(n-1))`