Conic constant

The conic constant, also called Schwarzschild constant, in addition to the radius of one of the two parameters with which a cone -section in size and shape can be specified. Displaying by means of conic sections and conical constant vertex radius plays a role in the specification of the form of aspheric lenses and optical mirrors.

Symmetrical to the x- axis conic line through the origin of the coordinate system can be represented by the following formula:

• R = radius of curvature at the zero point
• K = conic constant

Here, the conic constant defines the shape of the line. For k = 0, there is a circular line, which corresponds to rotation about the x- axis of a ball-shaped ( spherical ) surface. If k is different from zero, curves or surfaces which differ from the circular or spherical shape result:

If the conic constant k less than or equal to zero, so it is with the numerical eccentricity of the conic section line in the following context:

The representation of the conic lines in this form has the advantage that can be selected by variation of k surfaces with different characteristics, without changing the point of intersection of the curve with the x-axis for the calculation of the optical surfaces. This feature it shares with the vertex equation of the conic sections. In contrast to the vertex equation rotation ellipsoids can use this formulation not only flat, but also ( with a positive k) and high ellipses, and thus not only prolate, oblate also be treated.