Light Reflection and Optical Properties of a Parabola

This GeoGebra applet dynamically demonstrates the optical reflection properties of a parabola. Users can interactively adjust the initial emission point P_0 and the first reflection point I_0 on the parabola to observe the changing path of the reflected light rays. The model combines geometric and algebraic objects such as parabolas, vectors, lines, and sequences to visually illustrate the focal reflection principle and the trajectories of multiple reflections. By dragging the interactive points, students can explore how a ray originating from an arbitrary point in the plane reflects off the parabolic curve and subsequently passes through (or aligns with) the focus, thereby confirming the defining optical property: any ray directed toward the focus reflects parallel to the axis of symmetry, and conversely, any incoming ray parallel to the axis reflects through the focus. The applet also traces the sequence of successive reflection points, allowing learners to visualize iterative reflection paths and appreciate the underlying symmetry. This interactive exploration bridges analytic geometry and conic section theory, reinforcing the connection between the algebraic equation of the parabola and its geometric reflection behavior. The applet is well-suited for classroom instruction on conic sections, ray optics, and vector-based geometric modeling, enabling students to form and test conjectures through direct manipulation rather than passive observation.