If an object far away from a convex mirror moves towards the mirror, the image also moves. Does it move faster, slower or at the same speed as compared to the object?

#### Solution

The image of the object moves slower compared to the object. It can be explained using the mirror formula :

\[\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\]

We know that for a convex mirror, the object distance (*u*) is positive, image distance (*v*) is negative and the focal length (*f*) is also negative. Thus mirror formula of a convex mirror is:

\[\frac{1}{u} - \frac{1}{v} = - \frac{1}{f}\]

As *u* = +ve

\[\frac{1}{v} - \frac{1}{f} > 0\]

\[\frac{1}{v} > \frac{1}{f}\]

\[v < f\]

Therefore, the image is always formed within the focal length of the mirror. Thus, the distance moved by the image is much slower than the distance moved by the object.