Question

A point object O is kept at a distance of 30 cm from a convex lens of power + 4D towards its left. It is observed that when a convex mirror is kept on the right side at a distance of 50 cm from the convex lens, the image of the object O formed by the lens-mirror combination coincides with the object itself. Calculate the focal length of the convex mirror.

Answer 1

Focal length of the convex lens = 1/P m

Let a be the position of the image, I, of the object formed by the convex lens alone. We then have

Hence, the distance of the image (formed by the convex lens alone) from the convex mirror,would be (150-50) cm, i.e. 100 cm. This distance equals the radius of curvature of the convex mirror.

Hence the focal length of the convex mirror equals 100/2, i.e. 50 cm.