A concave mirror possesses a focal length of 20 cm . Determine the position or positions of an object such that the image-size is double the object-size.

Step-by-step solution

Given the focal length of the concave mirror, f = -20 cm . The magnification produced by a mirror is given by m = f f - u . Since the image size is double the object size, the magnification can be either m = -2 (real image) or m = +2 (virtual image). Case 1: For a real image, m = -2 -2 = -20 -20 - u 40 + 2u = -20 2u = -60 u = -30 cm Case 2: For a virtual image, m = +2 2 = -20 -20 - u -40 - 2u = -20 -2u = 20 u = -10 cm The object can be placed at 10 cm or 30 cm from the mirror.