Question

A camper is trying to start a fire by focusing sunlight onto a piece of paper. The diameter of the sun is 1.39 × 10⁹ m, and its mean distance from the earth is 1.50 × 10¹¹ m. The camper is using a converging lens whose focal length is 13.6 cm. (a) What is the area of the sun's image on the paper? (b) If 0.361 W of sunlight pass through the lens, what is the intensity of the sunlight at the paper?

Answer 1

Given data,

Diameter of sun = 1.39 × 10⁹ m

Diameter of earth = 1.50 × 10¹¹ m

a)

We know that,

magnification = - di/do

= - (0.136) / (1.50 × 10¹¹)

                         = - 9.06 * 10^-13

image height =   9.06 * 10^-13 x  1.39 × 10⁹

                           = 1.26 * 10^-3 m

The area of the sun's image on the paper = 3.14 * (1.26 * 10^-3 )²

                                                                   = 4.98 * 10^-6 m²

b)

Intensity of the sunlight at the paper =   0.361 / (4.98 * 10^-6 )

                                                           = 7.24 * 10⁴ W/m²