A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is :

Step-by-step solution

Given R = 30 cm So, f = R 2 = + 15 cm For convex mirror, virtual image is formed for real object. Thus, magnification m = 1 2 The magnification can be written as m = - v u . . . 1 Equation (1) implies that 1 2 = - v u ⇒ v = - u 2 The relation between the object distance, image distance and the focal length of the mirror is given by 1 f = 1 v + 1 u . . . 2 Equation (2) implies that 1 15 = 1 - u 2 + 1 u = - 1 u ⇒ u = - 15 cm