gbaldwinod@gmail.com

8/7/2019 1:47:31 PM
Crossed Cylinder Resultants
It is often useful to know the meridian of maximum axial refraction when combining the effects of two spherical cylinders at an oblique axis. To do this, we need to describe how their axial radii of curvature change with various meridional cross sections, and find expressions of those axial radii of curvature that are additive in terms of refraction. We then need to find the maximum sum of those expressions in terms of the meridional axis. Meridional cross sections of a spherical cylinder are ellipses, (until they become parallel lines along the cylinder axis). Finding the axial radii of these ellipses would be difficult. Assuming a spherical cylinder is a parabolic cylinder, (and assuming cross sections of parabolas are parabolas until they become a line along the cylinder axis), allows for a much simpler determination of the axial radii of curvature of meridional cross sections. The attached course works with these assumptions in order to provide approximations of axial radii of curvature for meridional cross sections of spherical cylinder. It also then uses expressions of these axial radii of curvature that are additive in terms of refraction, and demonstrates how to find the maximum sum of those expressions in terms of the meridional axis.
