An object is placed at a distance of 30 cm in front of a convex lens of focal length 20 cm. A convex mirror is placed coaxially 20 cm behind the lens. If the final image formed by the combination coincides with the object itself, the focal length of the convex mirror is :

Step-by-step solution

For the convex lens: Object distance, u = -30 cm Focal length, f = +20 cm Using the lens formula, 1 v - 1 u = 1 f 1 v - 1 -30 = 1 20 1 v = 1 20 - 1 30 = 1 60 v = +60 cm The convex lens forms an image 60 cm to its right. The convex mirror is placed 20 cm behind the lens. The image formed by the lens acts as a virtual object for the mirror, located at a distance of 60 - 20 = 40 cm behind the mirror. For the final image to coincide with the object, the rays refracted by the lens must strike the convex mirror normally.