Understanding multiple reflections in two plane mirrors by building computer simulations

摘要

In this article we investigate how students can build and use, in high-school Physics lessons, various interactive simulations aiming to a better understanding of the phenomenon of multiple reflections in two intersected plane mirrors. The applets achieved with GeoGebra allow changing the angle between the mirrors, the position of the source object and the position of the first reflexion point of a successively reflected ray of light. The applets provide a dynamic representation of the images of a movable object and also a representation of a reflected ray, highlighting the relation between the positions of the images and the extensions of a reflected ray. After discussing the positioning of the images of the point-like objects, we will address the same problem for some colourful polygonal shapes, resulting in kaleidoscopic figures. Finally, using GeoGebra , the students can simulate the movement of a point-like body that collides elastically against two walls forming an arbitrary angle, based on the analogy between the trajectory of the body and the path of a successively reflected ray in two plane mirrors. By building and using simulations students have the opportunity to make connections between their Math and Science knowledge, developing their skills in solving interdisciplinary problems.