A point object is placed at a distance of 30 cm from a convex lens of focal length 20 cm . A convex mirror of radius of curvature 40 cm is placed coaxially at a distance of 40 cm behind the lens. The position of the final image formed after reflection from the mirror and subsequent refraction through the lens is:

Step-by-step solution

For the first refraction through the convex lens: u₁ = -30 cm , f_L = +20 cm Using the lens formula: 1 v₁ - 1 u₁ = 1 f_L 1 v₁ - 1 -30 = 1 20 1 v₁ = 1 20 - 1 30 = 1 60 v₁ = +60 cm The first image is formed 60 cm behind the lens. Since the convex mirror is placed 40 cm behind the lens, this image acts as a virtual object for the mirror, located 20 cm behind it. For the reflection from the convex mirror: u_M = +20 cm (virtual object) The focal length of the convex mirror is f_M = R 2 = +40 cm 2 = +20 cm . Using the mi