Simulation of Optical Reflection Properties of a Circular Paraboloid

This GeoGebra applet dynamically simulates the optical reflection properties of a circular paraboloid using 3D vectors and surface commands. By constructing incident light rays and normal vectors, it demonstrates how parallel rays reflect off the parabolic surface and converge at the focal point. The interactive 3D visualization allows students to rotate, zoom, and adjust parameters in real time, observing how the geometry of the paraboloid determines the path of reflected rays. The model visually illustrates the principles behind satellite receivers, solar concentrators, and other real-world engineering applications that rely on the unique reflective properties of parabolic surfaces. By combining spatial analytic geometry with sequence commands, this applet serves as an effective cross-disciplinary teaching tool for both solid geometry and optics physics. Students can explore the mathematical proof that any incoming ray parallel to the axis of symmetry of a paraboloid will reflect through the focus, reinforcing the connection between algebraic representations and geometric behavior in three-dimensional space. This interactive approach helps learners build intuition about how abstract mathematical concepts manifest in physical phenomena.