It can be shown that the caustic generated by rays re C from a light source O (caustic of C relative to O) is equivalent to finding the evolute of the orthotomic of C relative to O.
* Step 2: Next, select the curves and click on 'Orthotomic Curve', the picture should look like Figure 6.
* Step 3: Now choose the Family of Orthotomic Normals, the picture should look like Figure 7:
Step 4: Click on the Caustics and note the following graph, we see that the caustic curve is the set of centers of curvature of the family of orthotomic normals of a given curve relative to O (the red or center dot).
The orthotomic curve of the ellipse relative to the origin, 0, can be shown (see ) to be
We plot the original ellipse (in green or inner ellipse), its orthotomic curve (in blue or outer ellipse), and its caustic curve, can be shown to be the curve shown in red (or in the center of the inner ellipse), together in Figure 9.
(2) Picking another point B on [C.sub.1], we obtain another orthotomic curve (shown in orange in Figure 5).
As B approaches C, the orange orthotomic curve approaches the black orthotomic curve.
(3) The sharp corner (cusp) of the black orthotomic occurs at the inflection point of [C.sub.2]: This can be experimented with [Geometry Expression].
(1) for a fixed point C on [C.sub.1] (light source at a point on [C.sub.1]), the orthotomic curve of [C.sub.2] relative to C is shown in black in Figure 6.
(2) Picking another light source B on [C.sub.1], we obtain another orthotomic curve (shown in orange in Figure 6).
As B [right arrow] C, the orange orthotomic curve [right arrow] the black orthotomic curve.