Question

A transparent slab of thickness d has a refractive index $n\left(z\right)$ 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 $n\left(z\right)$
• B. $n_1\sin {\theta }_i=(n_2-n_1)\sin {\theta }_f$
• C. $n_1\sin {\theta }_i=n_2\sin {\theta }_f$
• D. $l$ is independent of $n_2$

Answer 1

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

$l$ is independent of $n_2$

Since, Snell's law of refraction is valid at each boundary.
So, $n_{1}sin{\theta }_i=n_{2}sin{\theta }_f$

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

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

Answer is A, C and D.