Question

A man is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $10cm$. 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 suns 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

Answer: (D)

Magnification for 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,
$d=m\times 1.39\times 10^9$
$=6.67\times 10^{-13}\times 1.39\times 10^9$
$=9.27\times 10^{-4}m$