Conic section equation

Description

In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K.

The equation for a conic section with apex at the origin and tangent to the y axis is as shown here.

This formulation is used in geometric optics to specify oblate elliptical (K > 0), spherical (K = 0), prolate elliptical (0 > K > −1), parabolic (K = −1), and hyperbolic (K < −1) lens and mirror surfaces. When the paraxial approximation is valid, the optical surface can be treated as a spherical surface with the same radius.

Some non-optical design references use the letter p as the conic constant. In these cases, p = K + 1.

Related formulas

Variables

yy axis (dimensionless)
Rradius of curvature at x = 0 (dimensionless)
xx axis (dimensionless)
Kconic constant (dimensionless)