Distance between two slits is d. Wavelength of light is `lambda`. There is a
source of light S behind `S_2` at a distance `D_1`. A glass slab of thickness t and
refractive index `mu` is kept in front of `S_1.` Find.

(a) Net path difference at point P at an angular position `theta`.
(b) Write the equation for finding two angular positions corresponding to second order
minima `(y_2 and y_2')`.
If ` theta ` in part (b) does not come out to be small, then find two y-coordinates corresponding
to them.

Explanation

(a) `Deltax_1 = SS_1-SS_2 = ((d//2)(d))/D_1 `
` =d^2/(2D_1)`(Using `Deltax=(yd)/D`)
` Deltax_2= d sin theta `
` Deltax_3 = (mu -1)t `
` :. Deltax_"net" = (Deltax_1 + Deltax_3)~ d sin theta`
` = { (d^2/(2D_1)+(mu-1)t}~d sin theta`
(b) Corresponding to second order minima, net path difference should be `(3lambda)/2`. So, let `theta_1 and theta_2` be
the two angular positions, then
{ d^2/(2D_1) + (mu-1)t} - dsin theta_1 = (3lambda)/2 `
` and d sin theta_2 -{d^2/(2D_1) + (mu - 1)t} = (3lambda)/ 2 `
From these two equations, we can find `theta_1 and theta_2.`
` (c) Even if theta is not small, we can write`
` tan theta = y/D_2`
` :. y= D_2tantheta `
` Therefore, two y-coordinates are `
` y_1 = D_2 tan theta_1 `
and ` y_2 = D_2 tan theta_2 ` .