Question

A candle flame of length $3\text{cm}$ is placed at a distance of $3\text{m}$ from a wall. How far from the wall must a concave mirror be placed in order that it may form an image of flame $9\text{cm}$ high on the wall?

• A. $425\text{cm}$
• B. $500\text{cm}$
• C. $450\text{cm}$
• D. $650\text{cm}$

Answer 1

The correct option is C $450\text{cm}$


Let the mirror is placed at a distance $x$ from the wall.

Given :
$h=3\text{cm}$
$h^{\prime }=-9\text{cm}$

Here,
$u=-(x-3)$
$v=-x$

Magnification is given by,

$m=\frac{-v}{u}=\frac{h^{\prime }}{h}$

$\Rightarrow \frac{-(-x)}{-(x-3)}=\frac{-9}{3}$

$\Rightarrow x=3(x-3)$

$\Rightarrow x=\frac{9}{2}\text{m}=450\text{cm}$

Hence, option $\left(C\right)$ is the correct answer.