An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm . On the other side of the lens, a convex mirror is placed at its focus such that the image by the combination coincides with the object itself. What is the focal length (in cm) of the convex mirror?

Step-by-step solution

​ The retrace of the path after reflection from mirror rays after refraction from lens must incident towards the centre of curvature of the mirror Image by lense    1 v - 1 u = 1 f ⇒ 1 1 0 + 2 f m - 1 - 1 5 = 1 1 0 1 1 0 + 2 f m = 1 1 0 - 1 1 5 ⇒ 1 1 0 + 2 f m = 3 - 2 3 0 1 0 + 2 f m = 3 0 ⇒ f m = 1 0 cm