Consider a ray of light incident from air onto a slab of glass (refractive index n) of width d, at an angle θ. The phase difference between the ray reflected by the top surface of the glass and the bottom surface is

Time taken by purple ray to travel through a slab of reflective index n is given

The speed of light will decrease due to resistance given by medium; therefore it is given by c/n. And from snell’s law we already know a relation between n, r and θ. This is given by

But the option given in question requires a relation between θ and n, therefore we need to convert sin(r) into a suitable form. This could be done using simple trigonometric identity.

And we know sin �²r can be converted into sin²θ form using snell’s law relation.

Now for time T, phase difference is given 2π, therefore for ∆time, it will be given by

And c*T=λ. Therefore,

After re-arranging terms, we get

Now important thing to note is that when a wave from rarer medium get reflected by denser medium it suffers a phase difference by π. But when a wave from denser medium gets reflected by rarer medium no such phase difference is observed. Therefore net phase difference is given by