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 $n_1 and n_2 \left(>n_1\right),$ 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 angle ${\theta }_f$ with a lateral displacement $\mathcal{l}$ . Which of the following statement(s) is (are) true?

• Correct answer
  A

  $\mathcal{l}$ is independent of $n_2$
• Correct answer
  B

  $\mathcal{l}$ is dependent on n (z)
• C

  $n_1\sin {\theta }_i=\left(n_2-n_1\right)\sin {\theta }_f$
• Correct answer
  D

  $n_1\sin {\theta }_i=n_2\sin {\theta }_f$

Hence, the correct answer is options: 'A', 'B', 'D'.