Physics · Geometrical Optics

JEE Main 2025 — 22 January, Morning Shift — Question 60

Given is a thin convex lens of glass (refractive index $\mu$ ) and each side

having radius of curvature R. One side is polished for complete reflection. At what

distance from the lens, an object be placed on the optic axis so that the image gets

formed on the object itself.

Answer: D

$\quad \mathrm{P}_{\mathrm{eq}}=2 \mathrm{P}_{\ell}+\mathrm{P}_{\mathrm{m}}$

$-\frac{1}{\mathrm{f}_{\mathrm{Q}}}=\frac{2}{\mathrm{f}_{\ell}}-\frac{1}{\mathrm{f}_{\mathrm{m}}}$

$=\frac{4(\mu-1)}{R}-\frac{2}{-R}=\frac{1}{R}(4 \mu-4+2)$

$-\frac{1}{\mathrm{f}_{\mathrm{eq}}}=\frac{1}{\mathrm{R}}(4 \mu-2)$ $\Rightarrow \frac{1}{\mathrm{f}_{\mathrm{eq}}}=\frac{-1}{\mathrm{R}}(4 \mu-2)$

$f_{e q}=\frac{R}{2}$ $R=2 f_{\text {eq }}=-2\left(\frac{R}{4 \mu-2}\right)=\frac{-R}{(2 \mu-1)}$

Answer key and solution verified before publishing.

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