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Paraboloid Focus

Mathematics

★Exhibit Content: Parabolic reflection, geometric laws of parabolic focus, optical reflection analogized to mechanical reflection science popularization interactive experience ★Interaction: Manual ball dropping for mechanical trajectory observation interaction ★Operation: Drop the elastic ball vertically through the small hole at the top center of the transparent cover. The ball falls freely and hits the parabolic base at the bottom. Observe how the ball rebounds and accurately hits the bell hanging at the top. Repeat multiple times to verify the law. ★Exhibit Description: "Parabolic Focus" is a circular tabletop science exhibit that integrates analytic geometry and reflection laws, and is a recommended exhibit by KexMall. The exhibit features a white and blue circular floor-standing operation table with a yellow sealing rubber ring at the center. Above it is a cylindrical high-transparency acrylic dustproof protective cover. Inside, the bottom is a standard rotating parabolic base, and a metal bell hangs at the center of the top of the protective cover. It comes with elastic experimental balls and a science explanation sign. When the ball falls parallel to the symmetry axis of the paraboloid and hits the curved surface, all rebound trajectories converge to the focus of the paraboloid (the bell's position), visually analogizing the optical property of parallel light rays reflecting off a paraboloid and converging at the focus, transforming abstract geometric reflection laws into intuitive mechanical collision phenomena. ★Scientific Principle: 1. Geometric definition: A paraboloid is formed by rotating numerous parabolas with the same focus and directrix around the symmetry axis; all incident light rays parallel to the symmetry axis, after reflection off the paraboloid surface, must all converge at the unique focus of the paraboloid. 2. Mechanical analogy: The trajectory of a ball falling vertically is equivalent to an incident light ray parallel to the symmetry axis. The ball collides elastically with the parabolic base, and the collision reflection law is exactly the same as specular reflection of light. Therefore, after rebounding, all balls converge at the focus and accurately hit the bell hanging at the focus; this principle is widely used in searchlights, satellite antennas, solar concentrators, and other equipment.

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Principle Display: ★★★★ Interaction Effect: ★★★★ Ease of Installation: ★★★★★ Durability: ★★★★ Overall Rating: ★★★★★

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