For a plane mirror, if an object moves with a velocity 'v' towards the mirror, then the image moves with a velocity 2v. How?

We know that, for a plane mirror, the distance of image formed in the mirror is same as the distance of the object from the mirror.

Distance of object = u

Distance of image = -u (as the image is formed on the other side)

Thus, distance between the object and its image = 2u

Now if the object is approaching the mirror with a speed v, distance travelled by it in a unit time = v units

The new distance between mirror and object = u - v

Distance between the object and its image = 2(u-v)

We see that in a unit time, the distance between the image and the object is reduced by 2v units.

Thus, the speed of image w.r.t object = 2v