Question

An object 3 cm high is placed at a distance of 8 cm from a concave mirror which produces a virtual image of the mirror. Calculate the focal length of the mirror.
(i) What is the focal length of the mirror ?
(ii) What is the position of image ?
​

Answer 1

Explanation:

h1 = 3cm, u = -8cm, h2 = 4.5 (virtual image)

(i) we know that

m = h2/h1 = 4.5/3 = 1.5

and

m = - (v/u)

⇒ 1.5 = - (v/(-8))

⇒ v = 1.5 × 8 = 12 cm

We have

1/v + 1/u = 1/f

⇒ 1/12 + 1/(-8) = 1/f

⇒ 1/f = 1/12 – 1/8 = (2 – 3)/24 = - (1/24)

∴ f = - 24 cm

(ii) v = 12 cm

So, the image is formed 12 cm behind the concave mirror.