A concave mirror forms a virtual image of size twice that of the object placed at a distance 5 cm from it. Find (a) the focal length of the mirror (b) position of the image.

Distance of the object (u) = 5 cm (negative)

Magnification (m) = 2 (positive for the virtual image)

m = – v\over - 5

⇒ 2 = – v\over - 5

⇒ v = 2 × 5 = 10 cm

Hence, the image is formed 10 cm behind the mirror.

Mirror formula:

⇒ –1\over 5 + 1\over 10 = 1\over f

⇒ 1\over f = -2 + 1\over 10

⇒ 1\over f = -1\over 10

⇒ f = – 10 cm

Hence, focal length of the mirror = 10 cm

(b) The position of the image is 10 cm behind the mirror