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))`, as shown in the figure. A ray of light is incident with angle `theta_(i)`, from medium 1 and emerges in medium 2 with refraction and `theta_(f)`, with a lateral displacement l.

Which of the following statement(s) is (are) true ?

Options

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

Answer

A, B

Explanation

Clearly there is no role of `n_(2)` in deciding value of 1 and hence option (a) is correct.
Using Snell.s law `mu sin theta= const`, we can understand that option (b) is correct.
Bending of light in medium will depend on how n(z) varies with the height. Hence, option (c) is wrong. We can understand that if option (b) is correct then (d) cannot be correct. Option (d) is wrong. Only options (a) and (b) are correct.