Conic constant

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. For negative K it is given by the formula 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

Kconic constant (or Schwarzschild constant) (dimensionless)
eeccentricity (dimensionless)