Parabolic Car Headlamp: Reflection and Geometric Construction

This example demonstrates the application of a parabola in car headlamp design, showing how parallel light rays reflect off the parabolic surface and converge at the focus. The core mathematical concepts include the focus and directrix of a parabola, the law of reflection, and tangent properties. The construction uses GeoGebra commands such as OrthogonalLine, Point, Line, Tangent, Mirror, Intersect, Ray, and Vector, with objects like F (focus), g (directrix), c (parabola), and others to build the model. It is suitable for high school or early college students to understand the optical properties of conic sections, and can serve as interdisciplinary material combining mathematics and physics.