A plate of thickness t made of a material of refractive index `mu` is placed in front of one of the slits in a double slit experiment. (a) Find the changes in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the center of the fringe pattern zero ? Wavelength of the light used is `lamda`. Neglect any absorption of light in the plate.

Options

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

Answer

c

Explanation

Intensity at the center will be zero if path difference is `lambda // 2`. Thus is,
`(mu - 1) t = (lambda)/(2)`
or `t = (lambda)/(2(mu - 1)`