Putting a slab of refractive index [math]\mu[/math] and width [math]D[/math] in front of slits in YDSE.

Sep 2019
If I put a slab of some material whose refractive index is \(\displaystyle \mu\) and width is \(\displaystyle D\),

SEND 11.29.07 PM.png In the figure you can see that I have placed the slab just after the slits. So, when rays gonna come out of the slab they will bend away from normal (here I'm assuming that the material of the slab is optically denser than the air) and due to this bend they will intersect at P' and if the slab were to be absent they would have met at P. So, a pattern at P has shifted to P' but what is the mathematics of it? How to derive equations for path difference in this situation? Do we draw a perpendicular from \(\displaystyle S_1\) to \(\displaystyle S_2P\) like usual, but \(\displaystyle S_2P\) is not a single line it gets bent just after the slab. How should I begin?
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