In YDSE arrangement as shown in the figure, fringes are seen on screen using monochromatic source S having wavelength `3000Å` (in the air). `S_(1) and S_(2)` are two slits separated by d = 1 mm and D = 1 m. 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.

In order of get central maxima at the centre of the screen, the thickness of the slab `("in "mum)` required is :

Options

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

Explanation

`beta=(lambdaD)/(n_(2)d)=(3000xx10^(-10)xx1xx2)/(3xx1xx10^(-3))=2xx10^(-4)m =0.2 m`