A point object is placed on the principal axis at a distance of 40 cm in front of a convex lens L₁ of focal length 20 cm . A concave lens L₂ of focal length 15 cm is placed coaxially to the right of L₁ such that the final image of the object is formed at infinity. The distance between the two lenses is _________ cm .

Step-by-step solution

For the first lens L₁ (convex): u₁ = -40 cm f₁ = +20 cm Using the lens formula, 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -40 = 1 20 1 v₁ = 1 20 - 1 40 = 1 40 v₁ = +40 cm The intermediate image I₁ is formed 40 cm to the right of L₁ . This image acts as an object for the second lens L₂ . For the second lens L₂ (concave): The final image is formed at infinity, so v₂ = . f₂ = -15 cm Using the lens formula, 1 v₂ - 1 u₂ = 1 f₂ 1 - 1 u₂ = 1 -15 u₂ = +15 cm This means the object for L₂ (which is I₁ ) must be a virtual object located 15