A convex lens of focal length 20 cm and a concave lens of focal length 10 cm are placed in contact. An object is placed 40 cm in front of this lens combination. At what distance from the combination will the image be formed?

Step-by-step solution

First, find the equivalent focal length ( F_ eq ) of the lens combination. For the convex lens, f₁ = +20 cm . For the concave lens, f₂ = -10 cm . 1 F_ eq = 1 f₁ + 1 f₂ 1 F_ eq = 1 20 - 1 10 = 1 - 2 20 = - 1 20 cm ⁻¹ So, F_ eq = -20 cm (the combination acts as a concave lens). Next, apply the thin lens formula to find the image position ( v ). Object distance, u = -40 cm . 1 v - 1 u = 1 F_ eq 1 v - 1 -40 = 1 -20 1 v + 1 40 = - 1 20 1 v = - 1 20 - 1 40 = -2 - 1 40 = - 3 40 cm ⁻¹ v = - 40 3 cm The negative sign indica