The educational proposal focuses on the investigation of the recursive properties of the phenomenon of light reflection in a circular cavity within the framework of geometric optics. The research targets primary and secondary school students and is based on an experiential approach: the reflection trajectory within a circular cavity is reproduced and studied. By this experimental activity primary school students may gain familiarity with the geometric and recursive properties of light reflection using ruler and compass constructions. Middle school students can enhance these skills by analyzing and verifying the incommensurability properties of real numbers, leading to the interdisciplinary construction of regular polygons from component triangles. Finally, high school students can extend this study to trigonometric periodic functions, can analyze the application of the induction principle underlying the recursive property of reflection within the mirror, and can generate computer images of trajectories.