Using the POV raytracer to illustrate physics and math concepts

The POV raytracer is a free program that can be used to build virtual computer models that are then photographed using a virtual camera. The computer uses the known laws of optics, together with some clever computer shortcuts, to produce photorealistic images. The POV raytracer can be used to make purely artistic images, but it can also be used to help visualize complicated physical and mathematical concepts. It can also be used to teach students about the interaction of light and matter.
I should point out that POV has a very steep learning curve. You should not expect to sit down and produce high quality three-dimensional images within a matter of minutes. However, once you have mastered POV, it is possible to create some really remarkable images within a short amount of time.

POV is very useful for illustrating three-dimensional physical and mathematical phenomena. I have some simple tutorials illustrating how to visualize matrices and construct polyhedra

Before I discuss how to use POV for scientific purposes, I should emphasize that it can be used purely for creative art. One of my favorite POV artists is Gilles Tran who has created some remarkable works of art, including the following:

Note that Gilles Tran often provides free POV models so you can experiment with his works of art and build your own.

Now for some more scientific references.

The video below shows a wave traveling through the blue medium towards the green medium. The incident wavefronts can be seen in the form of the shadows they cast on the surface of the blue medium. The colored balls initially move parallel to the incident wave. You can think of them as the heads of surfers riding the wave. When they encounter the boundary at the green medium, the colored balls are reflected and travel parallel to the reflected wave. The wave velocity in the green medium is significantly higher than the velocity in the blue medium, and the angle of incidence is sufficiently large to prevent the waves from propagating into the green medium. This phenomenon is known as total internal reflection and is usually depicted using ray optics without any light entering the fast (green) medium. Nonetheless, there is a disturbance present in the green medium that decays exponentially with distance. This disturbance is known as an evanescent wave. The incident and reflected waves give rise to an interference pattern with maxima that move parallel to the surface of the blue-green boundary. If the blue medium is a piece of photographic film, then the maxima create a series of lines within the film. When developed, these lines form a reflection hologram.

Paul Nylander has created some wonderful physics images including this image, which appeared on the cover of the September 2009 issue of Physics Today and inspired my 3D dipole image.

He has also created some impressive math artwork.

Friedrich Lohmueller has created a very nice set of POV-ray tutorials and examples that will help you get started.

Mike Williams has created a POV isosurface tutorial. Isosurfaces are three-dimensional mathematical surfaces. These can be very useful for imaging very complicated mathematical surfaces.

Mike Kost has an organized set of POV tutorial links that will help the beginner get started.