An object of height 5 cm is placed perpendicular to the principal axis at a distance of 30 cm in front of a coaxial two-lens system. The system consists of a convex lens L₁ of focal length 20 cm and a second convex lens L₂ of focal length 10 cm placed 45 cm to the right of L₁ . The object is placed to the left of L₁ . The height of the final image formed by the system is _________ cm .

Step-by-step solution

For the first lens L₁ (convex): u₁ = -30 cm 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 = 1 60 v₁ = +60 cm The transverse magnification for L₁ is m₁ = v₁ u₁ = 60 -30 = -2 . The intermediate image I₁ is formed 60 cm to the right of L₁ . Since the distance between the lenses is 45 cm , I₁ lies 60 - 45 = 15 cm to the right of L₂ . This acts as a virtual object for L₂ . For the second lens L₂ (convex): u₂ = +15 cm f₂ = +10 cm Using the lens formula, 1 v₂ - 1 u₂ = 1 f₂ 1