A converging lens having a focal length of 15 cm and a converging mirror with a focal length of 10 cm are positioned 50 cm apart along a common principal axis. At what location on the principal axis must a point source be situated such that the two images are formed at the identical position?

Step-by-step solution

Let the point source be placed at a distance x from the lens. The distance of the point source from the mirror is 50 - x . Two images are formed by the optical system for an observer looking through the lens: one by the direct refraction of light through the lens, and another by the reflection of light from the mirror followed by refraction through the lens. For these two final images to form at the identical position, the light in both paths must act as identical objects for the lens. This means the intermediate i