A converging mirror M₁ , a point source S , and a diverging mirror M₂ are configured as shown in the figure. The source is located at a distance of 30 cm from M₁ . Each mirror has a focal length of 20 cm . Taking into account only the images produced by at most two reflections, it is observed that one image coincides with the source itself. Determine the distance separating the two mirrors.

Step-by-step solution

For the converging (concave) mirror M₁ , the focal length is f₁ = -20 cm . For the diverging (convex) mirror M₂ , the focal length is f₂ = +20 cm . Let the distance between the two mirrors be d . Consider the first reflection at M₁ : The object (source S ) is at a distance of 30 cm from M₁ , so u₁ = -30 cm . Using the mirror formula for M₁ : 1 v₁ + 1 u₁ = 1 f₁ 1 v₁ - 1 30 = - 1 20 1 v₁ = 1 30 - 1 20 = - 1 60 v₁ = -60 cm The first image I₁ is formed 60 cm in front of M₁ . Now, consider the second reflection at M₂ :