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# In a YDSE with $d= 1mm$ and $D= 1m$ slabs of $(t= 1 \mu m , \mu =3)$ and $(t=0.5\;\mu m , \mu =2)$ are introduced in front of upper and lower slit respectively . Then the shift in fringe pattern is :-

(a) 3 mm upwards (b) 1 mm upwards (c)2 mm upwards (d)1.5 mm upwards

Optical path for light coming from upper slit $S_1$ is
$s_1P + 1 \mu m (3-1) =s_1 P + 2 \mu m$
Similarly optical path for light coming from $s_2$ is
$s_2P + 0.5 \mu m (2-1) =s_2 P + 0.5 \mu m$
Path difference : $\Delta P= (s_2 P +0.5 \mu m)-(s_1P +2 \mu m)$
$\qquad= (s_2P-S_1P)-1.5 \mu m$
for central bright fringe $\S_2P-S_1P =0$