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 $n _{2}\left(> n _{1}\right)$, 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 $l .$ Which of the following statement(s) is(are) true?

• A. $l$ is dependent on $n (z)$
• B. $n _{1} \sin \theta_{1}=\left( n _{2}- n _{1}\right) \sin \theta_{ f }$
• C. $n _{1} \sin \theta_{1}= n _{2} \sin \theta_{ f }$
• D. $l$ is independent of $n _{2}$

Answer 1

Answer: (D)

$l$ is independent of $n _{2}$

Answer 2

By Snell's Law
$n _{1} \sin \theta_{1}= n _{2} \sin \theta_{f}$
$l$ will depend on angle of refraction which depends on refractive index
$l$ does not depend on $n _{2}$ as $l$ is defined upto the instant when ray emerge from slab.