An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm . Another convex lens Q is now placed 15 cm right of lens P . If the focal length of lens Q is 15 cm , the final image is _______.

Step-by-step solution

For lens P : 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -15 = 1 10 1 v₁ = 1 10 - 1 15 = 1 30 v₁ = 30 cm Magnification m₁ = v₁ u₁ = 30 -15 = -2 The image formed by lens P acts as a virtual object for lens Q . Since the distance between the lenses is 15 cm , the object distance for lens Q is: u₂ = 30 - 15 = +15 cm For lens Q : 1 v₂ - 1 u₂ = 1 f₂ 1 v₂ - 1 15 = 1 15 1 v₂ = 2 15 v₂ = 7.5 cm The positive sign indicates that the final image is real and formed 7.5 cm to the right of lens Q . Magnification m₂ = v₂ u₂ = 7.5 15 = 1 2 Total