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# Department of Science, Math, & Technology

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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. Cheers, 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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