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