Figure shows a convex lens placed in contact with a plane mirror. An axial point object is placed at a distance O at a distance,
OC = 20cm.

As the image I of the object coincides with O, the rays refracted first from the lens and then refracted by the plane mirror must be retracing their path. This would happen when rays refracted by the convex lens fall normally on the mirror I.e, the refracted rays form a beam parallel to principal axis of the lens. Hence the object O must be at the focus of the convex lens.
f = CO = 20 cm.