A candle is placed 20 cm from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is 12 cm away from the object, what is the focal length of the convex mirror?

For convex mirror, u+v=12×2=24cm(because for plane mirror, distance of object = distance of image). Also, here for the convex mirror u : 20 cm, therefore ν = 4 cm. Hence, using for plane mirror image distance =12 cm 1v+1u=1f  ⇒ 14+1-20=1f We find f = 5 cm.Plane mirror is to be placed between the object and the convex mirror.