YDSE with two different mediums

1. The problem statement, all variables and given/known data
Consider the scheme of YDSE as shown in fig filled with transparent of refractive indices ##n_1## and ##n_2## respectively.The slits are at a distance d apart. Find:

1. Location and width of central maxima.

2. Condition for constructive and destructive inteference

3. Fringe width above and below O.

2. Relevant equations

3. The attempt at a solution
I have never encountered such kind of setup for YDSE so I am not sure if the following is correct.

Consider the rays shown in attachment 2. I am thinking that if the refracted ray is extended backwards, it meets the cardboard with slits at point P. I can consider point P as the "effective" second slit. So I need the distance between the slit ##S_1## and this point i.e (x+d/2).

From Snell’s law and trigonometry, I found ##x=\frac{n_1d}{2n_2}##. Hence, the central maxima would lie on the perpendicular bisector of line joining ##S_1## and P i.e at a distance of ##d/4(1+n_1/n_2)##. The central maxima is at distance ##(d/4)(1-n_1/n_2)## from O. Is this correct?

Any help is appreciated. Thanks!

Attached Images
File Type: png YDSE1.png (7.4 KB)
File Type: png YDSE2.png (24.9 KB)

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