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 alternately where 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.
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 alternately where 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.