If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm , the focal length of the mirror must be :

Step-by-step solution

Let object be at a distance x cm from the pole. Then, distance of image from the pole will be = 15 - x . Given: Magnification, m = 2 = - v u ⇒ 2 = - ( 15 - x ) - x ⇒ 2 x = 15 - x ⇒ 3 x = 15 ⇒ x = 5 cm Now, Distance of the image from the pole = 15 - x = 15 - 5 = 10 cm Therefore, v = 10 cm From mirror formula: 1 f = 1 v + 1 u = 1 10 + 1 ( - 5 ) = 1 - 2 10 = - 1 10 ⇒ f = - 10 cm