 #jsDisabledContent { display:none; } My Account | Register | Help Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:

# Conic constant

Article Id: WHEBN0001977696
Reproduction Date:

 Title: Conic constant Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Conic constant

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

K = -e^2, \,

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

y^2-2Rx+(K+1)x^2=0

where K is the conic constant and R is the radius of curvature at x = 0.

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.