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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?

1. 9.2 × 10⁻⁴ m
2. 6.5 × 10⁻⁵ m
3. 6.5 × 10⁻³ m
4. 1.24 × 10⁻⁴ m

Correct answer: 9.2 × 10⁻⁴ m

Solution

The diameter of the Sun's image can be calculated using the formula for angular magnification: d' = f × (D / R), where f is the focal length of the lens, D is the diameter of the Sun, and R is the distance of the Sun from the Earth. Substituting the values: d' = 0.1 × (1.39 × 10⁹ / 1.5 × 10¹¹) = 9.2 × 10⁻⁴ m.

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