An object if placed at a distance of 15cm from a convex lens of focal length 10cm on the other side of the lens, a convex mirror is placed at its foxus such that the image formed by combination coincides with the object itself. Find the focal length of concave mirror.

Explanation

For retracing of ray, ray must fall normally on mirror i. e., toward the center of curvature.
`(1)/(v)-(1)/(u)=(1)/(f),u=-15`
`(1)/(v)+(1)/(15)=(1)/(10),f=10cm`
`v=30 cm`
For mirror `(1)/(v) +(1)/(v)=(1)/(f),u=2f`
`(1)/(v)+(1)/(2f)=(1)/(f)rArrV=2f`
Hence, from the ray diagram,
`2f=30-10`
`f=10cm`