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Reflective property of a parabola. The reflective property states that if a parabola can reflect light, then light that enters it travelling parallel to the axis of symmetry is reflected toward the focus. This is derived from geometrical optics, based on the assumption that light travels in rays. Consider the parabola y = x 2. Since all ...
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid , that is, the surface generated by a parabola revolving around its axis.
(The parabolas are orthogonal for an analogous reason to confocal ellipses and hyperbolas: parabolas have a reflective property.) Analogous to confocal ellipses and hyperbolas, the plane can be covered by an orthogonal net of parabolas, which can be used for a parabolic coordinate system .
The reflective properties of the conic sections are used in the design of searchlights, radio-telescopes and some optical telescopes. [43] A searchlight uses a parabolic mirror as the reflector, with a bulb at the focus; and a similar construction is used for a parabolic microphone .
This also works the other way around: a parallel beam of light that is parallel to the axis of the paraboloid is concentrated at the focal point. For a proof, see Parabola § Proof of the reflective property. Therefore, the shape of a circular paraboloid is widely used in astronomy for parabolic reflectors and parabolic antennas.
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This property has optical and acoustic applications similar to the reflective property of a parabola (see whispering gallery). Additionally, because of the focus-to-focus reflection property of ellipses, if the rays are allowed to continue propagating, reflected rays will eventually align closely with the major axis.
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