A 5 mm high pin is situated at a distance of 15 cm from a convex lens of focal length 10 cm . Positioned 40 cm from the first lens and 55 cm from the pin is a second lens having a focal length of 5 cm . Identify the nature of the final image.

Step-by-step solution

For the first lens: 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -15 = 1 10 1 v₁ = 1 10 - 1 15 = 1 30 v₁ = 30 cm Magnification of the first lens, m₁ = v₁ u₁ = 30 -15 = -2 The image formed by the first lens acts as the object for the second lens. The distance between the lenses is 40 cm . Object distance for the second lens, u₂ = -(40 - 30) = -10 cm For the second lens: 1 v₂ - 1 u₂ = 1 f₂ 1 v₂ - 1 -10 = 1 5 1 v₂ = 1 5 - 1 10 = 1 10 v₂ = 10 cm Since v₂ is positive, the final image is real. Magnification of the second lens, m₂ = v₂ u₂