Question

A man 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 $1.39\times {10}^{9}m$ and its mean distance from the earth is $1.5\times {10}^{11}m$, the diameter of the sun's image on the paper is

• A. $3.1\times {10}^{-4}m$
• B. $6.5\times {10}^{-5}m$
• C. $6.5\times {10}^{-4}m$
• D. $9.2\times {10}^{-4}m$

Answer 1

The correct option is D $9.2\times {10}^{-4}m$

Magnification of convex lens, $m=\frac{-f}{f-u}$

Here, $f=10cm=10\times {10}^{-2}m,u=1.5\times {10}^{11}m$

$\therefore m=\frac{-10\times {10}^{-2}}{10\times {10}^{-2}-1.5\times {10}^{11}}=6.67\times {10}^{-13}$

$\therefore$ Diameter of the image,

$d=m\times 1.39\times {10}^9=6.67\times {10}^{-13}\times 1.39\times {10}^9=9.27\times {10}^{-4}m$
Hence, the correct option is $\left(D\right)$