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Prove that rays that reflect from a Parabolic Dish cut the Z axis in the same point?

  1. Dec 15, 2011 #1
    I have the following "Parabolic Dish" z=c(x^2+y^2)
    I have to prove that all the reflecting light rays that hit that dish go through the same point Q in the Z axis, and then I have to find said point Q.


    I've thought of reducing the problem to 2 dimensions. Started with the parabola y = ax^2. Tried to find the angle that some line x = c strikes the curve but couldn't find the correct angle. Maybe do some gradient magic?


    I'm unsure really, how to set it all together for a good proof, and how to finally find the point Q.

    Please help :)
     
  2. jcsd
  3. Dec 15, 2011 #2

    SammyS

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    Re: Prove that rays that reflect from a Parabolic Dish cut the Z axis in the same poi

    I doubt that this is the complete problem as given. The incident rays would all need to be parallel to the z-axis.
     
  4. Dec 15, 2011 #3
    Re: Prove that rays that reflect from a Parabolic Dish cut the Z axis in the same poi

    Ohh, yes, obviously they are indeed parallel :)
     
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