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_(i)`, from medium 1 and emerges in medium 2 with refraction angle `theta_(f)`with a lateral displacement l.
Which of the following statement(s) is (are) true?

Options

A. `n_(1)sintheta_(i)=n_(2)sintheta_(f)`
B. `n_(1)sintheta_(i)=(n_(2)-n_(1))sintheta_(f)`
C. l is independent of `n_(2)`
D. l is dependent of `n(z)`

Answer

A, C, D

Explanation

`n_(1)sintheta_(i)=n_(2)sintheta_(f)` [`:'` 1 and 2 interfaces are parallel]
1 depends on the refractive index of transparent slab but not on `n_(2)`. In fact `theta_(f)` depends of `n_(2)`.