Question

A real image of half the size of the object is obtained in a concave mirror with a radius of curvature of $40\text{cm}$. The distance of the object and that of its image from the mirror will be ______ and ______ respectively.

• A. $15\text{cm},30\text{cm}$
• B. $30\text{cm},15\text{cm}$
• C. $30\text{cm},60\text{cm}$
• D. $60\text{cm},30\text{cm}$

Answer 1

The correct option is D $60\text{cm},30\text{cm}$

Given, image formed is real.
$m=\frac{-v}{u}=-\frac{1}{2}\Rightarrow -\frac{u}{v}=\frac{1}{2}\Rightarrow v=\frac{u}{2}$
$\Rightarrow \frac{1}{u}+\frac{1}{v}=\frac{1}{f}\Rightarrow \frac{1}{u}+\frac{2}{u}=-\frac{1}{20}$ $[\because f=\frac{R}{2}]$
$\Rightarrow \frac{1+2}{u}=-\frac{1}{20}\Rightarrow u=-60\text{cm}$
$\therefore v=-30\text{cm}$ where $v$ is the image distance, $u$ is the object distance and $m$ is the magnification.