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.

Step-by-step solution

Image of the flame formed by the concave mirror on the wall will be real and inverted, hence magnification m ⁡ = I ⁡ O ⁡ = - 1 . 5 0 · 5 = - 3 m ⁡ = - v ⁡ u ⁡ = - 3 ∴ v = 3 u Using 1 v ⁡ + 1 u ⁡ = 1 f ⁡ 1 3 u ⁡ + 1 u ⁡ = - 1 1 . 5 f ⁡ = - 1 . 5 m 4 3 u ⁡ = - 1 1 . 5 ∴ u ⁡ = - 4 × 1 . 5 3 = - 2 m Thus the flame is at distance 2m from the mirror and v = 3 u = – 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.