Question

A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical (depth) distance inside slab; measured from top. The slab is placed between two media having uniform refractive index, n₁ and n₂ (> n₁) respectively. A ray of light is incident, at an angle θ_i , from medium 1, and emerges out, in medium 2; with refraction angle θ_f , and with a later displacement l . Which of the following statements is incorrect?

(1) l independent of n (z)

(2) n₁ sinθ_i = (n₂ - n₁) sinθ_f

(3) n₁ sinθ_i = n₂ sinθ_f

(4) l depends on n₂

Answer 1

(2) n₁ sinθ_i = (n₂ - n₁) sinθ_f

The lateral displacement depends on (i) n₁ and (ii) n₂ but is indepdent of n(z). The only incorrect statement is