Conic constant

Conic constant. October, 2022. Page Version ID: 1117462111

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 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 \textgreater 0), spherical (K = 0), prolate elliptical (0 \textgreater K \textgreater −1), parabolic (K = −1), and hyperbolic (K \textless −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.

@misc{noauthor_conic_2022,
	title = {Conic constant},
	copyright = {Creative Commons Attribution-ShareAlike License},
	url = {https://en.wikipedia.org/w/index.php?title=Conic_constant&oldid=1117462111},
	abstract = {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 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 {\textgreater} 0), spherical (K = 0), prolate elliptical (0 {\textgreater} K {\textgreater} −1), parabolic (K = −1), and hyperbolic (K {\textless} −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.},
	language = {en},
	urldate = {2024-04-26},
	journal = {Wikipedia},
	month = oct,
	year = {2022},
	note = {Page Version ID: 1117462111},
}

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