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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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I'm not the downvoter, but basically, this perfectly good question shows not effort on your part. What have you done to solve this problem? Note that if you hover your mouse over the downvote button, the first criterion is "This question does not show any research effort". So that could be it. –  Kaz May 9 '12 at 21:50
    
Just as a sense , it can reach to point B. I try to understand why it cannot reach? –  Mathlover May 9 '12 at 21:57

1 Answer 1

up vote 6 down vote accepted

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.

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