A converging beam of light is directed towards a point P. A concave lens of focal length 15 cm is placed in the path of the beam such that point P is 10 cm behind the concave lens. A convex lens of focal length 20 cm is placed 10 cm behind the concave lens. The final image formed by the combination is located at:

Step-by-step solution

For the first lens (concave lens): The converging beam is directed towards point P, which acts as a virtual object. Object distance, u₁ = +10 cm Focal length, f₁ = -15 cm Using the lens formula, 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 10 = 1 -15 1 v₁ = 1 10 - 1 15 = 3 - 2 30 = 1 30 v₁ = +30 cm The intermediate image is formed 30 cm behind the concave lens. This acts as a virtual object for the second lens. For the second lens (convex lens): Distance between the lenses, d = 10 cm Object distance for the convex lens, u₂ = v₁ - d