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$|AB|$ and $|BC|$ are mirror surfaces. The light beam starts from point A with $\beta$ angle to x axis as shown the picture below.

1) What is the condition of the system parameters to reach to point $B$ $(x_0,0)$ after reflections between mirrors?

2) What is the reach time that depends on $x_0,\beta,\alpha$ if the beam can reach point $B$?

Assumtions: Mirrors are perfect plane and there is no loss during reflections and the speed of light is $c$.

enter image description here

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    Just as a sense , it can reach to point B. I try to understand why it cannot reach?2012-05-09

1 Answers 1

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You can see that it will never reach the vertex by "folding out" the angle, that is, flipping it over itself in a clockwise manner. Doing so will make the beam of light streak across the "folded out" angles in a straight line. The reason for this is that it obeys the law of reflection.

folded out

In the above picture I have "folded out" $\angle ABC$ by flipping it over itself in a clockwise manner. Instead of reflecting, the line now goes through into the next "flipped out" angle. To prove that the resulting line must be a straight line, simply apply the relationships of the laws of reflections to the angles at $D$. There is only one way to make a beam from $A$ intersect $B$, and that is to make it point directly at $B$.

You can check out an example of flipping out the angle which involves a completely different problem here.