A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 × 109 m and its mean distance from the earth is 1.5 × 1011 m. What is the diameter of the sun's image on the paper? (a) 6.5 × 10 - 5 m (b) 12.4 × 10 - 4 m (c) 9.2 × 10 - 4 m (d) 6.5 × 10 - 4 m

Answer: (c). Sun is at infinity, so the image forms at the focus; the sun's angular size θ = D/L. Image diameter d = fθ = 0.1 × 1.39 × 10⁹1.5 × 10¹¹ d ≈ 9.27 × 10⁻⁴ m So the answer is (c) 9.2 × 10⁻⁴ m.

A boy is trying to start a fire by focusing sunlight on a piece of… | NEET 2008 (AIPMT)

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Spherical Surfaces & Thin Lenses

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 $\times$ 109 m and its mean distance from the earth is 1.5 $\times$ 1011 m. What is the diameter of the sun's image on the paper?

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Answer: (c)

Sun is at infinity, so the image forms at the focus; the sun's angular size $\theta = \frac{D}{L}$ .
Image diameter $d = f\theta = 0.1 \times \frac{1.39 \times 10^{9}}{1.5 \times 10^{11}}$
$d \approx 9.27 \times 10^{-4}$ m
So the answer is (c) $9.2 \times 10^{-4}$ m.

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