An object is placed at a distance of 30 cm in front of a convex lens of focal length 20 cm. A concave lens of focal length 10 cm is placed coaxially behind the convex lens at a distance d . If the final image formed by the combination is at infinity, the value of d is :

Step-by-step solution

For the convex lens: Object distance, u₁ = -30 cm Focal length, f₁ = +20 cm Using the lens formula, 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -30 = 1 20 1 v₁ = 1 20 - 1 30 = 3 - 2 60 = 1 60 v₁ = +60 cm The image formed by the convex lens acts as a virtual object for the concave lens. For the concave lens: The final image is at infinity, so v₂ = . Focal length, f₂ = -10 cm Using the lens formula, 1 v₂ - 1 u₂ = 1 f₂ 1 - 1 u₂ = 1 -10 0 - 1 u₂ = - 1 10 u₂ = +10 cm The virtual object is 10 cm to the right of the concave lens. Since i