Question

A spherical mirror forms an image of magnification $3$. The object distance, if focal length of mirror is $24cm$, may be

• A. $32cm,24cm$
• B. $32cm,16cm$
• C. $32cm$ only
• D. $16cm$ only

Answer 1

The correct option is B $32cm,16cm$

Magnification is 3 it may be +3 or -3

then $v=-3u$ or $v=+3u$

If $v=-3u$

From mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{-1}{3u}+\frac{-1}{u}=\frac{-1}{f}$

$u=\frac{4f}{3}=\frac{4\times 24}{3}=32cm$

If $v=+3u$

From mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{3u}+\frac{-1}{u}=\frac{-1}{f}$

$u=\frac{2f}{3}=\frac{2\times 24}{3}=16cm$

So $u=32$ cm or $16$ cm

option $B$ is correct