A convex lens of focal length 20 ~cm and a concave lens of focal length 40 ~cm are kept in contact along their principal axis. An object is placed at a distance of 60 ~cm in front of this lens combination. The position of the image formed by the combination is :

Step-by-step solution

First, we find the equivalent focal length F_ eq of the lens combination. The focal length of the convex lens is f₁ = +20 ~cm and that of the concave lens is f₂ = -40 ~cm . 1 F_ eq = 1 f₁ + 1 f₂ 1 F_ eq = 1 20 + 1 -40 = 2 - 1 40 = 1 40 ~cm ⁻¹ F_ eq = +40 ~cm Now, applying the thin lens formula for the combination: 1 v - 1 u = 1 F_ eq Given the object distance u = -60 ~cm (using sign convention): 1 v - 1 -60 = 1 40 1 v + 1 60 = 1 40 1 v = 1 40 - 1 60 = 3 - 2 120 = 1 120 ~cm ⁻¹ v = +120 ~cm The image is formed at a d