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.
(In reply to
re: Possible Solution by Jer)
Jer,
I'm glad you commented because I can make my point even more simply.
Rather than 'mirror image' which may be subject to interpretation, let's call the mapping of the second ray onto the first a 180 degree rotation. There is therefore a point of rotation to the mapping, and for the reasons I gave, it lies at the centre of the rectangle. The rays have to meet at that point, so by necessity the given ray must pass through it.
Let's now assume the rays started from adjacent corners, also leaving from each other's starting points. That would be a mirror image properly so-called, and in that case there would be a line of reflection halfway between the starting points splitting the rectangle into identical halves. The two rays would then meet on that line. I note that you made a somewhat similar observation in your own solution.
I'm not sure how the other issue you raise arises. it's given in the problem that the ray: after being reflected several times enters to the opposite corner it started. Cases where the rays don't exit the rectangle at all don't matter for the purposes of this problem.
Edited on July 1, 2021, 10:26 am
|
|
Posted by broll
on 2021-07-01 10:17:19 |
re(2): Possible Solution
