A converging lens with a focal length of 15 cm and a converging mirror with a focal length of 10 cm are positioned 50 cm apart, sharing a common principal axis. A point source is situated between the lens and the mirror, at a distance of 40 cm from the lens. Determine the locations of the two images formed.

Step-by-step solution

The light from the point source can form an image in two ways: by directly refracting through the lens, and by first reflecting from the mirror and then refracting through the lens. For the first image (formed directly by the lens): The source is at a distance of 40 cm from the lens. Using the lens formula 1 v₁ - 1 u = 1 f : 1 v₁ - 1 -40 = 1 15 1 v₁ = 1 15 - 1 40 = 8 - 3 120 = 1 24 v₁ = +24 cm The positive sign indicates that the image is formed on the side opposite to the object, which is away from the mirror. For