A hemispherical vessel is completely filled with a liquid of refractive index μ . A small coin is kept at the lowest point ( O ) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is .

Physics · Geometrical Optics

JEE Main 2025 — 28 January, Morning Shift — Question 53

A hemispherical vessel is completely filled with a liquid of refractive index $\mu$ . A small coin is kept at the lowest point $(\mathrm{O})$ of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point $E$ (at the level of the vessel) is $\qquad$ .

Option A:
$\sqrt{3}$
Option B:
$\frac{3}{2}$
Option C:
$\sqrt{2}$
Correct
Option D:
$\frac{\sqrt{3}}{2}$

Answer: C

Step-by-step solution

$\sin \mathrm{c}=\frac{1}{\mu}$

for $\mu \rightarrow$ least, $\mathrm{c} \rightarrow$ maximum

$\theta=\mathrm{c}=45$

$\mu=\frac{1}{\sin 45}=\sqrt{2}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Morning Shift
Subject: Physics
Chapter: Geometrical Optics
Topic: Refraction in a Medium with Variable Refractive Index

A thin prism P 1 with angle 4^∘ made of glass having refractive index 1.54 , is combined with another thin prism P 2 made of glass having…

Answer: C

Step-by-step solution

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