Concave and convex lenses are placed touching each other. The ratio of magnitudes of their power is 2: 3 . The focal length of the system is 30 cm . The focal lengths of individual lens are

Step-by-step solution

Power (P)= 1 f ...(i) Given, P _ concave P _ convex = 2 3 ...(ii) Let the focal length of the convex lens be f _ convex = f From (i) and (ii), f _ concave =- 3 2 f (- ve as lens is concave ) Using the equivalent focal length for two lenses in contact, we get aligned 1 f_ e q & = 1 f + 1 - 3 2 f 1 30 & = 1 f - 2 3 f & = 3 f-2 f 3 f^2 aligned aligned & 1 30 = 1 3 f & , f =10 ~cm & f _ convex =10 ~cm and f _ concave = -3 2 10=-15 ~cm aligned