JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Geometrical Optics

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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 ______.

Answer: 20

Solution

Parallel sunlight burns the paper fastest when the paper lies at the focus, so

f = 30 cm

. For a symmetric biconvex lens with each face of radius

60

cm, the lens-maker's formula gives

\frac{1}{f} = (μ - 1) (\frac{1}{60} - \frac{1}{- 60}) = (μ - 1) \frac{2}{60} = \frac{μ - 1}{30}

. Setting

\frac{1}{30} = \frac{μ - 1}{30}

gives

μ - 1 = 1

, so

μ = 2

. Comparing with

μ = \frac{α}{10}

, the value of

α

20

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Integer answer

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