Abstract

In most treatments of the reflecting properties of the conic sections, the properties are stated without proof. In this paper the conic sections are derived from first principles as surfaces which produce specific effects on light rays. For example, the ellipse is taken to be a surface which reflects all rays emanating from one fixed point in a plane through a second fixed point in the plane. Each of the conic sections defined in this way is described by a first-order differential equation of second degree. The differential equations are solved and are shown to produce the expected results. These derivations should prove useful in introductory optics courses to give students a better feel for the reflecting properties of the conic sections.

© 1989 Optical Society of America