The Law of Reflection states that when a ray of light reflects from a mirror-like surface, the angle of incidence is equal to the angle of reflection. (Ideal particles behave the same way, when they bounce off a surface with no loss of energy.) From this simple concept an amazingly rich variety of phenomena occurs when there are multiple reflections

Like lines in Euclidean geometry, rays of light have a direction but no width, and are straight in a uniform medium. The analysis of multiple reflections therefore involves nothing more than Euclidean geometry in two or three dimensions. Problems involving a large number of reflections and/or reflections on curved surfaces are both challenging and interesting mathematically because they can lead to very complex fractal or chaotic patterns.

A familiar example of multiple reflections is seeing a seemingly infinite number of images while standing between two parallel mirrors. Another well-known example would be the Kaleidoscope wherein three long mirrors produce repeated and symmetric patterns. Multiple reflections from curved surfaces are less familiar, but can be illustrated by stacking four silvered globes in a tetrahedral pattern.

This project will present several examples of multiple reflections and show how they can be understood by ray trace models based on nothing more than Euclidean geometry and the law of reflection.