Playing with caustic phenomena
On a sunny day in a well-filled cup of coffee one often can observe a caustic. This is the well-known curve that is produced by the reflection of rays of light in a circular mirror. The phenomena one observes depend on the angle of incidence and the height of the mirror. They can be described mathematically with epicycloids. Not so well-known are the caustics which result from multiple reflections. They can be easily obtained with circular cylindrical mirrors producing aesthetic epicycloids in the form of a heart. I will show how to create these caustics. The mathematical derivation is given. The graphical representation is possible in a few lines with mathematical program packets like MATHEMATICA.