Parabola Reflection: Tangent, Normal, and Symmetric Transformation

This GeoGebra example dynamically demonstrates the law of reflection on a parabola: when an incident ray strikes a point on the parabola, the reflected ray obeys the reflection law (angle of incidence equals angle of reflection), and the reflected ray is symmetric to the incident ray with respect to the normal at that point. Core mathematical concepts include tangent and normal lines to a parabola, reflection law, symmetry transformations, and angle measurement. The construction uses GeoGebra commands such as Point, Segment, Intersect, Tangent, OrthogonalLine, Mirror, Ray, and Angle to build the parabola p, moving point A, tangent c, normal d, incident ray b, reflected ray i, and angles α, β, with an animation slider to control speed and visualize how the reflection path changes as the point moves. This is suitable for middle school, high school, or college analytic geometry courses to illustrate the optical property of conic sections, symmetry transformations, and geometric construction, and can also be used to explore the geometric meaning of the focus and directrix of a parabola.