A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices `n_(1)` and `n_(2)(gtn_(1))`, `theta_(0)`, from medium 1 and emerges in medium 2 with refraction angle `theta_(t)`with a lateral displacement l.
Which of the following statement(s) is (are) true?

Options

A. `l` is independence of `n (Z)`
B. `n_(1) sin theta_(i) = (n_(2) - n_(1)) sin theta_(f)`
C. `n_(1) sin theta_(i) = n_(2) sin theta_(i) = n_(2) sin theta_(f)`
D. `l` is independence of `n_(2)`

Answer

C, D

Explanation

Snell's law, `n sin theta = constant`
`:. n_(1) sin theta_(i) = n_(2) = sin theta_(f)`
Further, lateral displacement `l` depends on `n_(1)` and `n(Z)`. But it is independence of `n_(2)`.
Choice (c ) and (d) are correct.