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 $n_1$ and $n_2$ $(>n_1)$, as shown in the figure. A ray of light incident with angle ${\theta }_i$ from medium 1 and emerges in medium 2 with refraction angle ${\theta }_f$ with lateral displacement $l$.
Which of the following statement(s) is (are) true?

• A. $l$ is dependent on n(z)
• B. $n_1\sin {\theta }_1=(n_2-n_1)\sin {\theta }_f$
• C. $n_1\sin {\theta }_i=n_2\sin {\theta }_f$
• D. $l$ is independent of $n_2$

Answer 1

Answer: (A), (C), (D)

$n_1\sin {\theta }_i=n_2\sin {\theta }_f$
$l$ is independent of $n_2$
$l$ is dependent on n(z)

$n_{1}sin{\theta }_i=n_{2}sin{\theta }_f$ since law of refraction is valid at each boundary.

$l$ is independent of $n_2$ since the lateral displacement occurs even before the light enters medium 2.

$l$ is dependent on n(z) since lateral displacement depends on the refractive index.

Answer is A,C and D.