Catacaustics for Some Graphs

mirror

-

1-

2

x

4

x

3

x

-x+

3

x

-

3

x

+

5

x

-

1/3

(

2

x

)

Sin[x]

3

Sin[x]

x



-Log[x]

lines

10

20

50

100

200

500

1000

Vertical rays are reflected off the graph of a function and the corresponding catacaustic is plotted. The envelope of reflected or refracted lines coming from a point source is called a catacaustic or a diacaustic, respectively. In this case the source is infinitely far above the graph and the lines reflect off the graph as off a mirror.