A parabolic reflector (or dish or mirror) is a reflective device used to collect or project energy such as light, sound, or radio waves. Its shape is that of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave traveling along the axis into a spherical wave converging toward the focus. Conversely, a spherical wave generated by a point source placed in the focus is transformed into a plane wave propagating as a collimated beam along the axis.
Parabolic reflectors are used to collect energy from a distant source (for example sound waves or incoming star light) and bring it to a common focal point, thus correcting spherical aberration found in simpler spherical reflectors. Since the principles of reflection are reversible, parabolic reflectors can also be used to project energy of a source at its focus outward in a parallel beam, used in devices such as spotlights and car headlights.
The parabolic reflector functions due to the geometric properties of the paraboloidal shape: if the angle of incidence to the inner surface of the collector equals the angle of reflection, then any incoming ray that is parallel to the axis of the dish will be reflected to a central point, or "focus". Because many types of energy can be reflected in this way, parabolic reflectors can be used to collect and concentrate energy entering the reflector at a particular angle. Similarly, energy radiating from the "focus" to the dish can be transmitted outward in a beam that is parallel to the axis of the dish.
In contrast with spherical reflectors, which suffer from a spherical aberration that becomes stronger as the ratio of the beam diameter to the focal distance becomes larger, the parabolic reflectors can be made to accommodate beams of any width. However, if the incoming beam makes a non-zero angle with the axis (or if the emitting point source is not placed in the focus), parabolic reflectors suffer from an aberration called coma. This is primarily of interest in telescopes because most other applications do not require sharp resolution off the axis of the parabola.
The principle of parabolic reflectors has been known since classical antiquity, when the mathematician Diocles described them in his book On Burning Mirrors and proved that they focus a parallel beam to a point. Archimedes in the third century BC studied paraboloids as part of his study of hydrostatic equilibrium, and it has been claimed that he used reflectors to set the Roman fleet alight during the Siege of Syracuse. This seems unlikely to be true, however, as the claim does not appear in sources before the 2nd century AD, and Diocles does not mention it in his book. Parabolic mirrors were also studied by the physicist Ibn Sahl in the 10th century. James Gregory, in his 1663 book Optica Promota (1663), pointed out that a reflecting telescope with a mirror that was parabolic would correct spherical aberration as well as the chromatic aberration seen in refracting telescopes. The design he came up with bears his name: the "Gregorian telescope"; but according to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one. Isaac Newton knew about the properties of parabolic mirrors but chose a spherical shape for his Newtonian telescope mirror to simplify construction. Lighthouses also commonly used parabolic mirrors to collimate a point of light from a lantern into a beam, before being replaced by more efficient fresnel lenses in the 19th century.
The most common modern applications of the parabolic reflector are in satellite dishes, reflecting telescopes, radio telescopes, parabolic microphones, and many lighting devices such as spotlights, car headlights, PAR Cans and LED housings.
A parabolic reflector pointing upward can be formed by rotating a reflective liquid, like mercury, around a vertical axis. This makes the liquid mirror telescope possible.
A mirage bowl or parabolic mirror wok is a toy consisting of two parabolic mirrors that are put together like a wok pan and a lid with a hole in it. The device produces upright real image (with the magnification 1) of an object placed on the bottom of it, which gives the optical illusion that something is in the hole of the lid (while actually it is at the bottom of the pan below).