Question

A candle flame $0.5 \, cm$ high is kept between a wall and a concave mirror of focal length $1.5 \, m$ such that its image $1.5 \, cm \, $ 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. $4 \, m$ , $ \, 6 \, m$
• B. $6 \, m$ , $7 \, m$
• C. $6 \, m$ , $8 \, m$
• D. $9 \, m$ , $7 \, m$

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