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Given a thin convex lens (refractive index \(\mu_2\) ), kept in a liquid (refractive index \({\mu }_{1},{\mu }_{1} [JEE …

Q1

Given a thin convex lens (refractive index \(\mu_2\) ), kept in a liquid (refractive index \({\mu }_{1},{\mu }_{1}<{\mu }_{2}\) ) having radii of curvatures \(\left|{\mathrm{R}}_{1}\right|\) and \(\left|{\mathrm{R}}_{2}\right|\). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

[JEE Main 2025, 23 Jan (Shift 1)]

a

\(\frac{{\mu }_{1}\left|{R}_{1}\right|\cdot {R}_{2}∣}{{\mu }_{2}\left(\left|{R}_{1}\right|+\left|{R}_{2}\right|\right)-{\mu }_{1}\left|{R}_{2}\right|}\)

b

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|\cdot \left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\left|{\mathrm{R}}_{1}\right|}\)

c

\(\frac{\left({\mu }_{2}+{\mu }_{1}\right)\left|{\mathrm{R}}_{1}\right|}{\left({\mu }_{2}-{\mu }_{1}\right)}\)

d

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|\cdot \left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(2\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\sqrt{\left|{\mathrm{R}}_{1}\right|\cdot \left|{\mathrm{R}}_{2}\right|}}\)

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