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Question
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.
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