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The Gaussian formula and spherical aberrations of the static and relativisticcurved mirrors are analyzed using the optical path length (OPL) and Fermat'sprinciple. The geometrical figures generated by the rotation of conic sectionsabout their symmetry axes are considered for the shapes of the mirrors. Bycomparing the results in static and relativistic cases, it is shown that thefocal lengths and the spherical aberration relations of the relativisticmirrors obey the Lorentz contraction. Further analysis of the sphericalaberrations for both static and relativistic cases have resulted in theinformation about the limits for the paraxial approximation, as well as for theminimum speed of the systems to reduce the spherical aberrations.

The Gaussian formula and spherical aberration of the static and moving curved mirrors from Fermat's principle