We have a rectangle with it sides being a mirror. A light Ray enters from one of the corners of the rectangle and after being reflected several times enters to the opposite corner it started. Prove that at some time the light Ray passed the center of rectangle.
Instead of one light ray, consider two, leaving each corner at the same time, and travelling at precisely the same angle in opposite directions. Note that their paths are identical, in that one is the 'mirror image' of the other.
At some point, P, they must cross. What can we say about P?
The two rays must have travelled the same distance at the same speed to arrive at that point. Furthermore, since the paths are 'mirror images' of each other, each ray must now trace out the path of the other. to escape the box. This means that each ray has completed exactly half of its journey. P is therefore exactly the same distance from the two entry corners.
Since the box is a rectangle, this means that P is the centre of the rectangle, as was to be proved.
Edited on June 30, 2021, 10:51 pm
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Posted by broll
on 2021-06-30 22:49:59 |
Possible Solution
