A concave mirror forms a real image of an object placed in front of it at a distance 30 cm, of size three times the size of object. Find (a) the focal length of mirror (b) position of image.

(a) Distance of the object (u) = 30 cm (negative)

Image height = 3 times the height of object

So, magnification (m) = 3 (negative for the real image)

m = – v\over - 30

⇒ – 3 = – v\over - 30

⇒ v = -3 × 30 = – 90 cm

Hence, the image is formed 90 cm in front of the mirror.

Mirror formula:

⇒ –1\over 30 – 1\over 90 = 1\over f

⇒ 1\over f = -3-1\over 90

⇒ 1\over f = -4\over 90

⇒ f = – 22.5 cm

Hence, focal length of the mirror = 22.5 cm

(b) The image is formed 90 cm in front of the mirror