Confocal

Encyclopedia

In geometry

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Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

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**confocal**means having the same fociFocus (geometry)

In geometry, the foci are a pair of special points with reference to which any of a variety of curves is constructed. For example, foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola...

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- For an optical cavity consisting of two mirrors, confocal means that they share their foci. If they are identical mirrors, their radius of curvatureRadius of curvature (optics)Radius of curvature has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis...

,*R*_{mirror}, equals*L*, where*L*is the distance between the mirrors.

- In conic sectionConic sectionIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...

s, it is said of two ellipseEllipseIn geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

s, two hyperbolaHyperbolaIn mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

s, or an ellipse and a hyperbola which share both foci with each other. If an ellipse and a hyperbola are confocal, they are perpendicularPerpendicularIn geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

to each other.

- In opticsOpticsOptics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, it means that one focusFocus (optics)In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...

or image point of one lens is the same as one focus of the next lensLens (optics)A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

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