Parabolic Reflection
Posted: Posted August 22nd, 2019
Edited August 22nd, 2019 by The Fly
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A ray of light comes straight vertically down at \(x=a\) and reflects off the parabola \(y = cx^2\) according
to the usual principle of reflection (where \( c > 0\)). It bounces off the parabola and crosses the y-axis
at some point \(y = b\). Find \(b\) in terms of \(c\) and show that it is the same point regardless of where
the light is incident (that is, is independent of \(a\)). Do not look up any resources - solve from scratch.

The Fly

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I have a guess at the answer but I haven't gotten all the way through the proof yet. Right now I have that the angle of reflection is

$$\theta = tan^{-1}(2ac)$$

Edited August 25th, 2019 by EN
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