A combination of concave and convex lens in contact is placed over a plane mirror. When a pin P  is placed as shown in figure, the image is formed at the position of pin itself. The focal length of a convex lens is  10cm. Then the focal length of concave lens is______cm

Since the image of the pin is formed at the position of the pin itself, therefore light rays incident on the plane mirror normally which means that the rays falling over the lens will emerge parallel to its principal axis. Hence, the object point itself is the focus of combined lens.Therefore focal length of combined lens is  F=40 cmIf f1 and  f2 are the focal lengths of convex and concave lens respectively.1F=1f1+1f2 1f2=1F−1f1  f2=Ff1f1−F=40×1010−40 =−403=13.333 cm  Negative sign indicates concave nature of the lens.