(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 u + 1\over v = 1\over f
⇒ –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