JEE Main 2026 — Apr 2, Shift 2 — Physics solution

JEE Main2026Apr 2, Shift 2Physics

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 $\frac{α}{10}$ . The value of $α$ is___ .

Your answer

Solution

Sunlight (parallel rays) focuses at the focal point, so $f = 30$ cm.

Lensmaker's formula for a biconvex lens with $R_{1} = + 60$ cm and $R_{2} = - 60$ cm: $\frac{1}{f} = (μ - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}}) = (μ - 1) \cdot \frac{2}{60}$ .

$\frac{1}{30} = \frac{μ - 1}{30}$ , so $μ = 2 = \frac{20}{10}$ .

$∴ α = 20$ .

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