Question

A candle flame 3 cm high is placed at a distance of 3 m from a wall.how far from the wall must a concave mirror be placed so that it may form 9 cm high image of the flame on the same wall? Also find the focal length of the mirror.

Answer 1

Hi/Ho =$9/3=3X$

Then: Di/Do = 3 X → Di = 3 Do

Let distance between mirror and wall = Z. Then Z = Di (because image is on wall).

Then $Z=3$Do

But Do $+3=Z$→ Do + $3=3$Do → $3=2$Do → Do$=1.5m$ and Di$=4.5m$

Therefore, mirror must be placed at 4.5 m from wall.

Using mirror equation, we can calculate focal length: $1/f=1/1.5+1/4.5$ →

$f=4.5/4=1.125m$