Geometric and Optical Properties of a Parabolic Mirror

This GeoGebra example demonstrates the geometric and optical reflection properties of a parabolic mirror (parabola). It shows how light rays parallel to the axis of symmetry reflect off the parabolic curve and converge at the focus, and conversely, how rays originating from the focus reflect parallel to the axis. Core mathematical concepts include the parabola, tangent lines, normal lines (orthogonal lines), mirror symmetry, the law of reflection (angle of incidence equals angle of reflection), and the focal properties of conic sections. To construct this visualization, the example utilizes key GeoGebra commands such as Parabola to draw the curve, Tangent and OrthogonalLine to define the reflective surface and normal vectors, Mirror to generate reflected points (like C', D'), and Ray/Segment to trace light paths. Angles of incidence α and reflection β are marked using the Angle command, and Rotate is used for dynamic alignment. This tool is highly suitable for high school analytic geometry, physics optics courses, and university-level geometry classes studying conic sections and their practical applications in optics.