Physics · Geometrical Optics

JEE Advanced 2023 — Paper 2 — Question 18

A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from $n_{1}$ to $n_{2}$ over the height $h$ . Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Option A:
It will deflect up by an angle $\tan ^{-1}\left[\frac{\left(\mathrm{n}_{2}^{2}-\mathrm{n}_{1}^{2}\right) \mathrm{d}}{2 \mathrm{~h}}\right]$
Option B:
It will deflect up by an angle $\tan ^{-1}\left[\frac{\left(\mathrm{n}_{2}-\mathrm{n}_{1}\right) \mathrm{d}}{\mathrm{h}}\right]$ .
Correct
Option C:
It will not deflect
Option D:
The deflection angle depends only on $\left(\mathrm{n}_{2}-\mathrm{n}_{1}\right)$ and not on the individual values of $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ .
Correct

Answer: B, D

Step-by-step solution

Wavefront PQ at time ' t ' $\frac{\mathrm{n}_{2} \mathrm{~d}}{\mathrm{c}}=\frac{\mathrm{n}_{1} \mathrm{~d}}{\mathrm{c}}+\frac{\mathrm{x}}{\mathrm{c}}$ $\mathrm{x}=\mathrm{d}\left(\mathrm{n}_{2}-\mathrm{n}_{1}\right)$ $\tan \theta=\frac{\mathrm{x}}{\mathrm{h}}=\frac{\left(\mathrm{n}_{2}-\mathrm{n}_{1}\right) \mathrm{d}}{\mathrm{h}}$ $\theta=\tan ^{-1}\left[\frac{\left(\mathrm{n}_{2}-\mathrm{n}_{1}\right) \mathrm{d}}{\mathrm{h}}\right]$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2023
Paper: Paper 2
Subject: Physics
Chapter: Geometrical Optics
Topic: Refraction in a Medium with Variable Refractive Index