Question

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.

Answer 1

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`