Q. 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) 12.4 × 10⁻⁴ m
B) 9.2 × 10⁻⁴ m
C) 6.5 × 10⁻⁴ m
D) 6.5 × 10⁻⁵ m
Explanation
[Solution from source] The image forms in the focal plane, and the Sun and its image subtend the same angle at the lens: d = f × D/u = 0.10 × 1.39 × 10⁹/1.5 × 10¹¹ ≈ 9.3 × 10⁻⁴ m, closest to 9.2 × 10⁻⁴ m. 6.5 × 10⁻⁴ m would come from wrongly halving or mis-scaling the angular size. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.