  We find that the function that describes the surface of spherical aberration
free lenses can be used for both positive and negative refractive index media.
With the inclusion of negative index, this function assumes the form of all the
conic sections and expands the theory of aplanatic optical surfaces. There are
two different symmetry centers with respect to the index that create an
asymmetric relationship between positive and negative index lens profiles. In
the thin lens limit the familiar formulas for image position and magnification
hold for any index.
