Situated at a distance of 15 cm from a convex lens of focal length 10 cm is a 5 mm high pin. A second lens having a focal length of 5 cm is positioned 40 cm from the first lens and 55 cm from the pin. Determine the position of the final image.

Step-by-step solution

For the first lens: u₁ = -15 cm , f₁ = 10 cm Using the lens formula, 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -15 = 1 10 1 v₁ = 1 10 - 1 15 = 1 30 v₁ = 30 cm The image formed by the first lens acts as an object for the second lens. The distance between the lenses is 40 cm . Object distance for the second lens, u₂ = -(40 - 30) = -10 cm Focal length of the second lens, f₂ = 5 cm Using the lens formula again, 1 v₂ - 1 u₂ = 1 f₂ 1 v₂ - 1 -10 = 1 5 1 v₂ = 1 5 - 1 10 = 1 10 v₂ = 10 cm The positive sign indicates that the final image