Conic constant

In geometry, the conic constant (or Schwarzschild constant,[1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by

where e is the eccentricity of the conic section.

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

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.

This geometry-related article is a stub.

Ten different conic sections which open to the right from a common intersection point, at which point they have a common radius of curvature
An illustration of various conic constants