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Given a thin convex lens (refractive index μ_2 ), kept in a liquid (refractive index μ_1, μ_1 lt μ_2 ) having radii of curvatures |R_1 | and |R_2 |.…

JEE Main 2025 — Physics Optics

2025mcqmedium

Given a thin convex lens (refractive index μ2\mu_2μ2​ ), kept in a liquid (refractive index μ1,μ1<μ2\mu_1, \mu_1 \lt \mu_2μ1​,μ1​<μ2​ ) having radii of curvatures ∣R1∣\left|R_1\right|∣R1​∣ and ∣R2∣\left|R_2\right|∣R2​∣. 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?

Official previous-year question

Held on 23 Jan 2025 · Verified 6 Jul 2026.

Options

  1. A

    μ1∣R1∣⋅∣R2∣μ2(∣R1∣+∣R2∣)−μ1∣R2∣\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}_2\right|}μ2​(∣R1​∣+∣R2​∣)−μ1​∣R2​∣μ1​∣R1​∣⋅∣R2​∣​

  2. B

    μ1∣R1∣⋅∣R2∣μ2(∣R1∣+∣R2∣)−μ1∣R1∣\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|}μ2​(∣R1​∣+∣R2​∣)−μ1​∣R1​∣μ1​∣R1​∣⋅∣R2​∣​

  3. C

    (μ2+μ1)∣R1∣(μ2−μ1)\frac{\left(\mu_2+\mu_1\right)\left|\mathrm{R}_1\right|}{\left(\mu_2-\mu_1\right)}(μ2​−μ1​)(μ2​+μ1​)∣R1​∣​

  4. D

    μ1∣R1∣⋅∣R2∣μ2(2∣R1∣+∣R2∣)−μ1∣R1∣⋅∣R2∣\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|}}μ2​(2∣R1​∣+∣R2​∣)−μ1​∣R1​∣⋅∣R2​∣​μ1​∣R1​∣⋅∣R2​∣​

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