Two convex lenses, each having a focal length of 10 cm , are positioned at a separation of 15 cm with their principal axes coinciding. Determine the location of the virtual image produced by the lens system for an object located far away.

Step-by-step solution

For the first lens, the object is at infinity, so u₁ = - and f₁ = +10 cm . Using the lens formula: 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 - = 1 10 v₁ = +10 cm The image formed by the first lens acts as a real object for the second lens. Since the distance between the two lenses is 15 cm , the object distance for the second lens is: u₂ = -(15 - 10) = -5 cm For the second lens, f₂ = +10 cm . Applying the lens formula again: 1 v₂ - 1 u₂ = 1 f₂ 1 v₂ - 1 -5 = 1 10 1 v₂ + 1 5 = 1 10 1 v₂ = 1 10 - 1 5 = - 1 10 v₂ = -10 cm The negati