A man stands 10 m in front of a large plane mirror. How far must he walk before he is 5 m away from his image?
Initially, the distance between the man and the mirror is 10 m, then, the distance between the man's image and the mirror will also be 10 m. (because the image formed by a plane mirror is at the same distance behind it as it is between the object and the mirror).
Therefore, the distance between man and his image is 10 + 10 = 20 m
Now,
Distance between the man and his image is 5 m, which means that, the distance between man and the mirror = $\frac{5}{2}$ = 2.5 m.
As we know a plane mirror forms images of the object at the same distance behind it as it is between the object and the mirror (2.5 + 2.5 = 5 m).
Therefore, the distance he should walk = 10 m – 2.5m = 7.5 m towards the mirror.
Thus, the man must walk 7.5 m towards the mirror before being 5 meters away from his image.
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