A plane mirror of mass $m$ is tied to the free end of a massless spring of spring constant $k$. The other end of the spring is attached to a wall. The spring with the mirror held vertically to the floor can slide along it smoothly. When the spring is at its natural length, the mirror is found to be moving at speed $v$. The separation between the images of a man standing before the mirror, for the two extreme positions of the mirror, is