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conic constant : ウィキペディア英語版
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.
==References==

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