Question

A candle flame $0.5cm$ high is kept between a wall and a concave mirror of focal length $1.5m$ such that its image $1.5cm$ high is formed on the wall. Find the distance of candle from the wall and also the distance between the wall and the mirror.

• A. $4m$ , $6m$
• B. $6m$ , $7m$
• C. $6m$ , $8m$
• D. $9m$ , $7m$

Answer 1

Answer: (A)

Image of the flame formed by the concave mirror on the wall will be real and inverted, hence magnification

$m=\frac{I}{O}=\frac{-1\text{.}5}{0\cdot 5}=-3$
$m=-\frac{v}{u}=-3$
∴ $v=3u$
Using $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{3u}+\frac{1}{u}=-\frac{1}{1\text{.}5}$ $\left(f=-1\text{.}5\text{m}\right)$
$\frac{4}{3u}=-\frac{1}{1\text{.}5}$
∴ $u=\frac{-4\times 1\text{.}5}{3}=-2\text{m}$
Thus the flame is at distance 2m from the mirror and $v=3u=-6m$
Hence the distance between wall and mirror is 6 m. It implies that the distance between the flame and the wall will be 4m.