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 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, $f = 10\,cm= 10\times 10^{-2}\,m$
$u = 1.5\times 10^{11}\,m$
$\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,
$d = m\times 1.39 \times 10^9$
$= 6.67 \times10^{-13} \times 1.39 \times 10^{9}$
$ = 9.27 \times 10^{-4}\,m$