Physics · Geometrical Optics

JEE Main 2026 — 23 January, Morning Shift — Question 35

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media $A$ and $B$ are $2.4 \times 10^{8} \mathrm{~m} / \mathrm{s}$ and $2.7 \times 10^{8} \mathrm{~m} / \mathrm{s}$ respectively, then the value of critical angle is :

Option A:
$\cot ^{-1}\left(\frac{3}{\sqrt{13}}\right)$
Option B:
$\sin ^{-1}\left(\frac{9}{8}\right)$
Option C:
$\tan ^{-1}\left(\frac{8}{\sqrt{17}}\right)$
Correct
Option D:
$\cos ^{-1}\left(\frac{8}{9}\right)$

Answer: C

Step-by-step solution

$\mu_{\mathrm{A}} \sin \mathrm{c}=\mu_{\mathrm{B}} \sin 90$ $\Rightarrow \sin \mathrm{c}=\frac{\mu_{\mathrm{B}}}{\mu_{\mathrm{A}}}=\frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}$ $\therefore \sin c=\frac{2.4 \times 10^{8}}{2.7 \times 10^{8}}=\frac{8}{9}$ $\Rightarrow \tan c=\frac{8}{\sqrt{81-64}}=\frac{8}{\sqrt{17}}$ $c=\tan ^{-1}\left(\frac{8}{\sqrt{17}}\right)$

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Exam: JEE Main 2026
Paper: 23 January, Morning Shift
Subject: Physics
Chapter: Geometrical Optics
Topic: Introduction to Refraction of Light (Snell's Law)

A thin prism with angle 5^circ of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion…

Answer: C

Step-by-step solution

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