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Reflective Property of the Parabola
One of the most fascinating properties of the parabola is its reflective property, which is as follows: If a light source is placed at the focus of a parabola, after reflecting off the parabola, the rays of light will emerge as a correlated beam with all rays parallel to the symmetry axis of the parabola. Similarly, a parallel beam of light rays incident on a parabola will converge onto the focus after being reflected.
The three-dimensional analog of the reflective property of a parabola is realized for a paraboloid, the surface formed by rotating a parabola about its axis of symmetry. It is this property that is used in flashlights, headlights, and searchlights. In all of these devices, a point light source is placed at the focus of a parabolic mirror, resulting in a correlated beam of light emerging along the symmetry axis of the device. The opposite property is utilized in satellite dishes and reflecting telescopes, each of which involves a signal converging on the focus after being reflected.
Other conic sections enjoy reflective properties similar to the parabola. For instance, if a light source is placed at one focus of an ellipse, the rays will converge onto the other focus after being reflected. Any wave, including sound waves, may be substituted for light. Thus, a whispering gallery is an elliptic room in which sound waves converge onto a focus after emerging from a source at the other focus. A hyperbola also satisfies an interesting reflective property in which a point source at one focus, after being reflected, behaves as if it were at the other focus.
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