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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?
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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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