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Suppose I have a steel frame parabolic reflector with a handful of steel wire supports. The size is approximately 10m high and 20m in radius. Assume the gaps in the triangular trusses are roughly 3m.

Presumably, if I focus roughly 30Mhz radio signals at this structure they will reflect and be concentrated at a focal point some distance from the center of the dish.

Simple question: if I flip that structure upside down, and focus 30Mhz radiation centrally (so normal to the plane tangent to the minimum of the parabola), how will the radiation scatter?

I suppose an answer could range from simply “the signal will scatter”, to a more precise description of the scattering. There’s obviously a U(1) symmetry here, but it would be interesting to know how the power is distributed across the z-axis.

The analogy in the visible range is a convex mirror. The plain English answer would be “the image is distorted, and parts of the image look bigger or smaller. You can see across a wider angle.”

Thanks!

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    $\begingroup$ For the inside reflection, draw lines through the parabola. They show how a corresponding outside reflection would work. That may help you think about the answer. $\endgroup$
    – mmesser314
    Feb 19, 2022 at 17:09
  • $\begingroup$ If I draw parallel lines through, I suppose for the inside reflection, IIRC, you just look at the tangent, and then perhaps the outgoing angle is equal to the incoming angle measured w.r.t. the tangent line. The outgoing lines would presumably just go straight through the tangent line to the other side. The lines would be concentrated at the center, but then get sparser as the angle changes from 0-90deg, which I guess you'd measure w/ a derivative of the slopes of the outgoing lines w.r.t. angle. $\endgroup$ Feb 19, 2022 at 17:31

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If you use parallel rays thee scatter as if they would come from the focal point on the opposite side. if you have rays coming from one point, you can construct the scattered rays like coming from the imaginary picture of your source like in a convex mirror. You can use the same equations which are easy to find.

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  • $\begingroup$ So there are two focal points, the one on the concave side, and another on the convex side? Why would there be a focal point on the convex side? Could you provide the easy-to-find reference for light scattering off a convex mirror? Is the scattering independent of frequency? $\endgroup$ Feb 21, 2022 at 16:21
  • $\begingroup$ 1. reference: wikipedia. 2. use a spherical mirror, so you can construct every rays reflection with the angel of reflection to the radius. $\endgroup$
    – trula
    Feb 22, 2022 at 10:50
  • $\begingroup$ A spherical mirror sounds like a cool idea. Like a disco ball? $\endgroup$ Feb 23, 2022 at 11:31
  • $\begingroup$ the center Part of a parabolic mirror is well approximated by part of a sphere $\endgroup$
    – trula
    Feb 27, 2022 at 16:03

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