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Prove involving parabolic mirrors

  1. Feb 27, 2014 #1
    I'm having trouble with the following problem:

    "Consider the parabolic mirror given by the equation $z=x^2+y^2$. Show that when the rays of light that travel paralell to the $z$ axis pass through the same point when reflected."

    I'm familiar with the law of reflection but I'm stuck because I don't know how to apply vector calculus to this situation. I have tried to apply the law of reflection but I can't seem to get anywhere.

  2. jcsd
  3. Feb 27, 2014 #2


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    Gold Member

    You simply need to consider the equations of two straight lines:

    - a certain ray parallel to the axis, and see where it cuts the mirror
    - the ray reflected from there, according the the law of reflexion

    The picture below suggests what you have to do: simply follow the red path.

    Last edited: Feb 27, 2014
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