A ray of light travelling in air is incident at grazing incidence on a slab with variable refractive index, n `(y) = [ky^(3//2) + 1 ]^(1//2)` where `k=1 m^(-3//2)` and follows path as shown in the figure. What is the total deviation produced by slab when the ray comes out.

Options

A. `60^(@)`
B. `53^(@)`
C. `sin^(-1)(4//9)`
D. no deviation at all

Answer

D

Explanation

As n varies `'y'` , parallel slabs can be taken , and we kown in parallel slabs `n_(r) sin i_(r)` = constant . As `n_(1)sini_(1)` `=1xxsin90^(@)=1` = constant
`n_("final")=n_(air)=1`
`implies 1=1xxsin r_("final" implies r_("final")=90^(@)`
:. Deviation is zero.