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
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