A converging mirror M₁ , a point source S , and a diverging mirror M₂ are configured. 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 location of the image formed by a single reflection from M₂ .

Step-by-step solution

For the converging mirror M₁ , the focal length is f₁ = -20 cm and the object distance is u₁ = -30 cm . Using the mirror formula for M₁ : 1 v₁ + 1 u₁ = 1 f₁ 1 v₁ - 1 30 = - 1 20 v₁ = -60 cm Let the distance between the source S and the diverging mirror M₂ be x . The distance between the two mirrors is d = 30 + x . For the image to coincide with the source after two reflections (first from M₁ and then from M₂ ), the image I₁ formed by M₁ acts as a virtual object for M₂ . The distance of I₁ from M₂ is 60 - d = 60 - (