Maple Program

You may download the Maple programs from this page, but I'll describe them here and show some output displays.


I wrote two programs, one for the Cassegrain system and one for the Gregorian. Above you see a sample output. The parabola has a focus at y = 5. This is also one of the hyperbola's foci, (sometimes hereafter called the hyperbola's "first" focus). The hyperbola has another ("second") focus at y = -7. An arbitrarily chosen vertical ray is "reflected" by the program, and is seen to follow the expected path.


Here is another output; different curves and a different vertical ray. To work the program, you fire up Maple V, (a "must have" application) and open the file. I included instructions and annotations, in my own inimitable style. You are prompted to either accept the default values, or select your own altitude for the parabola's focus and the hyperbola's second focus. The program places the hyperbola's first focus coincident with the parabola's focus and it traces the curves according to your selections. You then choose a location, -9 < x < 9, for the vertical ray to enter.

Now (above) we have a sample output from the Gregorian program. It works just like the Cassegrain program. It's funny that it took just as long to write, however. I kept looking for shortcuts, using the code from the previous program. That might have been fine, had I not short cut on the thinking, too.

The problems with writing a program like this are not evident until you wade in. Whether the incoming ray meets the parabola above or below the focus affects the calculations, since the ray may have a positive or negative slope. It was also necessary to consider from which side of the origin the ray had entered. Another surprise was the need to determine if the ray could intersect the secondary reflector in two points. If this was possible, even where the curve was not traced, strange outputs resulted.

You may view the programs in ASCII form by clicking here and here, but this viewing leaves a lot to be desired. You would be much better served to download and run them on your own computer. Use your *->right<-* mouse button (not left) to click on the link. You will get the menu (from Netscape anyway) to download the files. From the menu, select the item saying, "Save link as.."

I invite you to make improvements. I intended to have rays enter randomly and simultaneously, rather than just one at a time. I'll get to that some day, unless you beat me to it.

Onward