Question

An object is placed at a dustance `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 1

The course of rays for image formation is shown in Fig. Clearly, image `I` formed by plane mirror is such that `MI = OM = 24 cm`

As convex mirror forms the image at `I` itself,
therefore, `v = PI = MI - MP`
`= MI - (OP - OM)`
`= 24 - 12 = 12 cm`
`u = OP = -36 cm`
`(1)/(f) = (1)/(v) + (1)/(u) = (1)/(12) - (1)/(36) = (3 - 1)/(36) = (2)/(36) = (1)/(18)`
`f = 18 cm , R = 2f = 2 xx 18 = 36 cm`.