A Concave lens is placed in contact with a . . .

Question :  A Concave lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

CBSE 2014 (Delhi)

Solution : 

From the figure, it is clear that the rays between the convex lens and plane mirror M are exact parallel. Hence they strike the plane mirror normally so they will be reflected back at an angle refraction of zero degrees and trace exactly the same path and finally forms the image at O. 

We know, when rays passes from the focus of a convex they become parallel to each other or when parallel rays passes through the convex lens then they passes through the focus. 
Hence O or I must be the focal length of the convex lens. 

Object Distance = Image Distance = 20 cm 

Hence, focal length of the convex lens = 20 cm