How to find the focal point of a parabolic dish using reflection

[gipc]

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 :)

 

[SammyS]

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 :)

I doubt that this is the complete problem as given. The incident rays would all need to be parallel to the z-axis.

 

[gipc]

Ohh, yes, obviously they are indeed parallel :)