Appendix K SKEW RAYS IN HYPERBOLOIDAL CONCENTRATOR

We shall prove that any ray aimed at the rim of the entry aperture is reflected to some point on this rim. Let *FF*′ in Figure K.1 be the diameter of the entry aperture, so that *F* and *F*′ are the foci of the hyperbolas in the plane of the diagram, and let *P* be a point on a hyperbola. The bisector *PR* of angle *FPF*′ is tangent to the hyperbola, and thus the tangent plane at *P* passes through *PR*. Any skew ray to the rim incident on the hyperbola at *P* passes through some point on the circle of which *FF*′ is the diameter and that is in a plane perpendicular to the diagram, and all such rays generate an oblique circular cone. We now draw *F*_{1}*F*_{1}′ through *R* to make the same angle with *PR*, as shown. A plane ...

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