Physics · Geometrical Optics

JEE Advanced 2025 — Paper 2 — Question 6

Two identical concave mirrors each of focal length $f$ are facing each other as shown in the schematic diagram. The focal length $f$ is much larger than the size of the mirrors.

A glass slab of thickness $t$ and refractive index $n_{0}$ is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source

$S$ is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on $S$ itself, which of the following distances between the two mirrors is/are correct

Option A:
$4 f+\left(1-\frac{1}{n_{0}}\right) t$
Correct
Option B:
$2 f+\left(1-\frac{1}{n_{0}}\right) t$
Correct
Option C:
$4 f+\left(n_{0}-1\right) t$
Option D:
$2 f+\left(n_{0}-1\right) t$

Answer: A, B

Step-by-step solution

$\frac{S-t}{2}+\frac{t}{2 n_{0}}=2 f$

$\mathrm{S}+\mathrm{t}\left(\frac{1}{\mathrm{n}_{0}}-1\right)=4 \mathrm{f}$

$\mathrm{S}=4 \mathrm{f}+\left(1-\frac{1}{\mathrm{n}_{0}}\right) \mathrm{t}$

Also $\frac{S-t}{2}+\frac{t}{2 n_{0}}=f$

$\mathrm{S}=2 \mathrm{f}+\left(1-\frac{1}{\mathrm{n}_{0}}\right) \mathrm{t}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2025
Paper: Paper 2
Subject: Physics
Chapter: Geometrical Optics
Topic: Miscellaneous Problems for different combinations