# A convex lens of focal length 10 cm forms a real image of an object placed at a distance of 20 cm from it. Midway between the convex lens and the position of the image a thin concave lens is introduced. The image formed now is at a distance of 5 cm away from the earlier position. What is the focal length of the concave lens? I solved it in the following way: Case-1 Let u, v and f be the object distance, image distance and the focal length of the convex lens. Here u = 20 cm, f = + 10 cm 1/v = 1/f – 1/u 1/v= 1/10 – 1/20 v = 20 cm Case- 2 Let u, v and f be the object distance, image distance and the focal length of the concave lens. Here u = - 10(virtual object), v = + 15 cm 1/f = -1/10 + 1/15 f = - 30 cm But the answer given in my book is – 5 cm.