Question

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 n₁ and n₂ (> n₁), as shown in the figure. A ray of light is incident with angle θ_i from medium 1 and emerges in medium 2 with refraction angle θ_f with a lateral displacement l.

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

(A) n₁ sinθ_i = n₂ sin θ_f 

(B) n₁ sinθ_i = (n₂ - n₁) sin θ_f 

(C) l is independent of n₂ 

(D) l is dependent on n (z)

Answer 1

(A) n₁ sinθ_i = n₂ sin θ_f 

(C) l is independent of n₂ 

(D) l is dependent on n (z)

From Snell’s Law

n₁ sinθ_i = n(d) sinθ_d = n₂ sinθ_f

The deviation of ray in the slab will depend on n (z) 

Hence, l will depend on n (z) but not on n₂