We know the conjugate focci relation for lens as follows
Inserting these in equation  we get
So the lens forms a real image at a distance of
It has been said that on placing a convex mirror 40 cm behind the lens, the final image coincides with object itself. This is possible only if retracing of rays is brought about by the reflection on convex mirror i.e the rays emerging from lens are incident on the convex mirror normally and it is possible if they are directed to the center of curvature of the mirror as shown in the ray diagram above.
So distance of radius of curvature from lens is
Hence the radius of curvature of mirror is
Again we know that the focal length of mirror
So the focal length of the mirror will be