Conic constant explained

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 $$K\; =\; -e^2,$$ where 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$$y^2-2Rx+(K+1)x^2\; =\; 0$$alternately$$x\; =\; \backslash dfrac$$where R is the radius of curvature at .

This formulation is used in geometric optics to specify oblate elliptical, spherical, prolate elliptical, parabolic, and hyperbolic lens and mirror surfaces. When the paraxial approximation is valid, the optical surface can be treated as a spherical surface with the same radius.

References

• Book: Smith, Warren J. . Modern Optical Engineering, 4th ed . . 2008 . 978-0-07-147687-4 . 512–515.

Notes and References

1. Rakich. Andrew . Jose M . Sasian . R. John. Koshel . Richard C. Juergens . 2005-08-18 . The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics . Novel Optical Systems Design and Optimization VIII. International Society for Optics and Photonics. 5875. 587501 . 10.1117/12.635041. 2005SPIE.5875....1R . 119718303.