A point object is placed on the principal axis of a convex lens of focal length 20 cm . A plane mirror is placed at a distance of 10 cm behind the lens. The light rays from the object pass through the lens, get reflected by the plane mirror, and then pass through the lens again. If the final image is formed at a distance of 40 cm in front of the lens, the distance of the original object from the lens is ____ cm .

Step-by-step solution

Let us trace the image formation backwards. The final image is formed after the second refraction through the lens at a distance of 40 cm in front of it. By sign convention, v₂ = -40 cm . Applying the lens formula for the second refraction: 1 v₂ - 1 u₂ = 1 f 1 -40 - 1 u₂ = 1 20 1 u₂ = - 1 40 - 1 20 = - 3 40 u₂ = - 40 3 cm This object for the second refraction is the image formed by the plane mirror, located 40 3 cm in front of the lens. Since the mirror is 10 cm behind the lens, this image is at a distance of 10 +