An object is placed at a distance of `36 cm` from a convex mirror. A plane mirror is placed inbetween so that the two virtual images so formed coincide. If the plane mirror is at a distance of `24 cm` from the object, find the radius of curvature of convex mirror.

Answer

36 cm

Explanation

Distance of image from plane mirror = distance of object from plane mirror. Therefore, for convex mirror, `u = -36 cm` and
`v = + (24 + 24 - 36) cm = + 12 cm`.
From `(1)/(f)=(1)/(v)+(1)/(u)=(1)/(12)+(1)/(-36)=(1)/(18)`
`f = 18 cm`
`R = 2f = 2 xx 18 cm = 36 cm`.