A ray of light travelling in air is incident at grazing incidence on a slab with variable refractive index, n `(y)` `=[k y^(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 know in parallel slabs
`n_(r) sin i_(r)`=constant, as `n_(1) sin i_(1) =1xxsin 90^(@) =1`=constant
`n_("final")=n_(air)=1`
`rArr 1=1xxsin r_("Final")`
`rArr r_("final") =90^(@)`
`:.` Deviation is zero.