At a distance of 15 cm from a convex lens of focal length 10 cm , a 5 mm high pin is placed. A second lens of focal length 5 cm is located 40 cm from the first lens and 55 cm from the pin. Calculate the size of the final image.

Step-by-step solution

For the first lens, using the lens formula: 1 v₁ - 1 u₁ = 1 f₁ Given u₁ = -15 cm and f₁ = +10 cm . 1 v₁ - 1 -15 = 1 10 1 v₁ = 1 10 - 1 15 = 3 - 2 30 = 1 30 v₁ = +30 cm Magnification of the first lens, m₁ = v₁ u₁ = 30 -15 = -2 For the second lens, the image formed by the first lens acts as the object. The distance between the lenses is 40 cm . Object distance for the second lens, u₂ = -(40 - 30) = -10 cm . Given f₂ = +5 cm . Using the lens formula: 1 v₂ - 1 u₂ = 1 f₂ 1 v₂ - 1 -10 = 1 5 1 v₂ = 1 5 - 1 10 = 2 - 1 10 =