Question

A candle flame 3cm high is placed at a distance of 3m from a wall. How far from the wall must a concave mirror be placed in order that it may form an inverted image of the flame of height 9cm on the wall? Also, determine the focal length of the mirror.

• A. 4.5 m, focal length = 1.125 m
• B. 2.5 m, focal length = 2.125 m
• C. 3.5 m, focal length = 2.25 m
• D. 5.5 m, focal length = 0.125 m

Answer 1

The correct option is A 4.5 m, focal length = 1.125 m

The candle of height AB = 3 cm is placed at a distance u from the concave mirror. Since the object is 3 meters from the wall, the image distance is
$v=u+3$
Since, the image is inverted, the magnification is
$m=-\frac{9}{3}=-3m=-\frac{v}{u}=-\frac{u+3}{u}\frac{u+3}{u}=3u=1.5m$
Therefore, the mirror must be placed at a distance of (1.5+3) = 4.5 m from the wall.
From mirror formula:
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\frac{1}{f}=-\frac{1}{4.5}-\frac{1}{1.5}=-\frac{4}{4.5}f=-1.125m$
Therefore, the focal length of the concave mirror is 1.125 m.