An object is placed in front of a concave mirror of focal length 20 cm such that it forms a real and magnified image. If the distance between the object and its image is 30 cm , the linear magnification produced by the mirror is :

Step-by-step solution

For a concave mirror forming a real image, both the object and the image are on the same side of the mirror (in front of it), so u and v are both negative. Since the image is magnified, the image distance is greater than the object distance ( |v| > |u| ). The distance between the object and the image is given as 30 cm . |v| - |u| = 30 -v - (-u) = 30 u - v = 30 v = u - 30 Given focal length f = -20 cm . Using the mirror formula: 1 f = 1 v + 1 u 1 -20 = 1 u - 30 + 1 u -1 20 = u + u - 30 u(u - 30) -u^2 + 30u = 20(2u -