In YDSE arrangement as shown in figure, fringes are seen on screen using monochromatic source S having wavelength 3000 Å (in air). `S_1 `and `S_2` are two slits seperated by d = 1 mm and D = 1m. Left of slits `S_1` and `S_2` medium of refractive index `n_1 = 2` is present and to the right of `S_1` and `S_2` medium of `n_2 = 3/2`, is present. A thin slab of thickness 't' is placed in front of `S_1` . The refractive index of `n_3` of the slab varies with distance from it's starting face as shown in figure.

Fringe width on the screen is

Options

A. `0.4mm`
B. `0.1mm`
C. `0.2mm`
D. `0.3mm`

Answer

B

Explanation

Area `(A) = mu_(3) (dx) = ((1+3)t)/(2) = 2t`
`beta = (lambda D)/(mu_(2)d) = (3000xx10^(-10)xx1xx2)/(3xx1xx10^(-3)) = 2xx10^(-4)m`
`beta = 0.2m`