A diverging lens with a focal length of 20 cm and a converging mirror with a focal length of 10 cm are arranged coaxially with a separation of 5 cm . At what distance should an object be placed such that a real image is formed at the location of the object itself?

Step-by-step solution

For the final image to form at the location of the object itself, the light rays must retrace their path after reflection from the mirror. This condition is satisfied if the rays from the lens strike the mirror normally, which requires the image formed by the lens to be at the center of curvature of the mirror. The focal length of the converging mirror is f_M = 10 cm , so its radius of curvature is R = 20 cm . The center of curvature is 20 cm in front of the mirror. Since the distance between the lens and the mirro