The lens combination as shown in the figure, consists of two lenses, L₁ and L₂ , of the focal lengths +10 cm and -10 cm, respectively. The position of the image formed is :

Step-by-step solution

For the first lens L₁ (convex lens): Object distance, u₁ = -30 cm Focal length, f₁ = +10 cm Using the lens formula, 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -30 = 1 10 1 v₁ + 1 30 = 1 10 1 v₁ = 1 10 - 1 30 = 3 - 1 30 = 2 30 = 1 15 v₁ = +15 cm The image I₁ formed by L₁ acts as a virtual object for the second lens L₂ . For the second lens L₂ (concave lens): Distance between the lenses, d = 3 cm Object distance for L₂ , u₂ = v₁ - d = 15 - 3 = +12 cm Focal length, f₂ = -10 cm Using the lens formula, 1 v₂ - 1 u₂ = 1 f₂ 1 v₂ - 1 12 =