A point object is placed at a distance of 60   cm from a convex lens of focal length 30   cm . If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40   cm from it, the final image would be formed at a distance of :

Step-by-step solution

first, for image formation from lens u = - 60   cm f = + 30   cm ⇒ v = u f u + f = - 60 × 30 - 60 + 30 = 60   cm this real image formed by lens acts as virtual object for mirror Real image from plane mirror is formed 20   cm in front of mirror, hence at 20   cm distance from lens. Now, for second refraction from lens, u = - 20   cm f = + 30   cm v = u f u + f = - 20 × 30 - 20 + 30 = - 60   cm So, final virtual image is 60   cm from lens, or 20   cm b