[UPSC IFoS 2015] Interference (Q194, 10M)

In Young's double-slit experiment, a thin mica sheet (refractive index $= 1 \cdot 5$ ) is introduced in the path of one of the beams. If the central fringe gets shifted by $0 \cdot 2\text{ cm}$ , calculate the thickness of the mica sheet. Assume separation between the two slits ( $d$ ) and between slit and source ( $D$ ) as $d = 0 \cdot 1\text{ cm}$ and $D = 50\text{ cm}$ .