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.

Question

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 ______. [2026]

Smart Achievers · Accepted Answer

(20)

$To burn in minimum time distance of paper must be at focus.$

$So f = 3 cm$

$Lens maker formula,$

$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{30} = (μ - 1) (\frac{2}{R})$

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

$μ = 2 \Rightarrow \frac{α}{10} = 2 \Rightarrow α = 20$

Solution

Q.
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 ______. [2026]

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Solution

Q. 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 α10. The value of α is ______. [2026]

Ans. (20) To burn in minimum time distance of paper must be at focus. So f=3 cm Lens maker formula, 1f=(μ-1)(1R1-1R2) 130=(μ-1)(2R) 130=(μ-1)(260) μ=2⇒α10=2⇒α=20

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