Constructing the Catacaustic of an Ellipse - Radial Rays

A light source at the radiant point S produces some radial light rays (in yellow). The rays are reflected by the ellipse, with semi-major axis [math]a[/math] and a semi-minor axis[math] b[/math]. If the rays have more than one intersection point with the ellipse, they are reflected at both points. The reflected rays and their continuations are shown in light blue. Definition: The envelope of the reflected rays by the ellipse is called the [i]catacaustic [/i]of the ellipse (also called [i]caustic[/i]). [list] [*]Drag the slider - "numberRays" to change the number of light rays. [*]Drag the slider - "d" to change the distance from the center of the ellipse to the radiant point. [*]Drag the slider -"α" to rotate the radiant point around the center of the ellipse. [*]Sliders a and b will change the dimensions of the ellipse. [/list]