Question

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 $1.39\times {10}^{9}m$ and its mean distance from the earth is $1.5\times {10}^{11}m$. What is the diameter of the Sun's image on the paper ?

• A. $6.5\times {10}^{-5}m$
• B. $12.4\times {10}^{-4}m$
• C. $9.2\times {10}^{-4}m$
• D. $6.5\times {10}^{-4}m$

Answer 1

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

Object distance, $u=1.5\times {10}^{11}m$

Image distance, $v==10cm=0.1m$

We know,

Magnification=$\frac{\upsilon }{u}=\frac{h_i}{h_0}$

$\Rightarrow \frac{0.1}{1.5\times {10}^{11}}=\frac{h_i}{1.39\times {10}^9}$

$h_i=\frac{1.39\times {10}^8}{1.5\times {10}^{11}}=9.2\times {10}^{-4}m$