Refraction law and Fermat principle: a project using the ant colony optimization algorithm for undergraduate students in physics

A programming project for undergraduate students in physics is proposed in this work. Its goal is to check the Snell-Descartes law of refraction using the Fermat principle and the ant colony optimization algorithm. The project involves basic mathematics and physics and is adapted to students with basic programming skills. More advanced tools can be used (but are not mandatory) as parallelization or object-oriented programming, which makes the project also suitable for more experienced students. We propose two tests to validate the program. Our algorithm is able to find solutions which are close to the theoretical predictions. Two quantities are defined to study its convergence and the quality of the solutions. It is also shown that the choice of the values of the simulation parameters is important to efficiently obtain precise results.