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 Earth is 1.5 × 10¹¹ m. What is the diameter of the image of the Sun on the paper?
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Question

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 Earth is 1.5 × 10¹¹ m. What is the diameter of the image of the Sun on the paper?

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G1 Physics · Accepted Answer

Step 1: The Sun subtends a small angular diameter α ≈ D_sun/L = (1.39 × 10⁹)/(1.5 × 10¹¹). Step 2: A distant object forms its image in the focal plane, diameter d ≈ fα. Step 3: d = 0.10 × 1.39 × 10⁹/(1.5 × 10¹¹) ≈ 9.27 × 10⁻⁴ m. Final answer: (A) 9.2 × 10⁻⁴ m.