TL;DR
This paper derives the fundamental equation for mirrors with arbitrary conic sections and demonstrates that only parabolic mirrors are free of aberration, and only for distant sources.
Contribution
It provides the first derivation of the object-image relation for conic-shaped mirrors and clarifies the aberration properties of parabolic surfaces.
Findings
Derived the first order mirror equation for conic sections.
Showed parabolic mirrors are aberration-free only for distant sources.
Established the unique aberration-free property of parabolic mirrors.
Abstract
The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.
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