If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is α/10 . The value of α is .

Physics · Geometrical Optics

JEE Main 2026 — 2 April, Evening Shift — Question 21

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at $30\mathrm{cm}$ above the paper. If the radius of curvature of the lens is $60\mathrm{cm}$ then the refractive index of the lens material is $\frac{\alpha}{10}$ . The value of $\alpha$ is ______.

Answer: 20

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Step-by-step solution

For minimum time, paper at focus: $f=30\mathrm{cm}$ . Lens maker: $\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$ for symmetric biconvex $R_1=60,R_2=-60$ → $\frac{1}{30}=(\mu-1)\left(\frac{1}{60}+\frac{1}{60}\right)=(\mu-1)\frac{1}{30}$ → $\mu=2$ → $\alpha=20$

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Exam: JEE Main 2026
Paper: 2 April, Evening Shift
Subject: Physics
Chapter: Geometrical Optics
Topic: Refraction at Curved Surface and Glass Sphere

One side of an equilateral prism is painted by a transparent material of refractive index n 2 . The refractive index of prism is 1.6. The…

Answer: 20

Step-by-step solution

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