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Optical Space
{{Unsourced, date=September 2013 Optical spaces are mathematical coordinate systems that facilitate the modelling of optical systems as mathematical transformations. An optical space is a mathematical coordinate system such as a Cartesian coordinate system associated with a refractive index In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac .... The analysis of optical systems is greatly simplified by the use of optical spaces which enable designers to place the origin of a coordinate system at any of several convenient locations. In the design of optical systems two optical spaces, object space and image space, are always employed. Additional intermediate spaces are often used as well. Optical spaces extend to infinity in all directions. The object space does not exist only on the "i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformation (function)
In mathematics, a transformation, transform, or self-map is a function ''f'', usually with some geometrical underpinning, that maps a set ''X'' to itself, i.e. . Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations. Partial transformations While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to partial functions, then a partial transformation is a function ''f'': ''A'' → ''B'', where both ''A'' and ''B'' are subsets of some set ''X''. Algebraic structures The set of all transformations on a given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative numbers, signed distances to the point from two fixed perpendicular oriented lines, called ''coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the ''Origin (mathematics), origin'' and has as coordinates. The axes direction (geometry), directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refraction, refracted, when entering a material. This is described by Snell's law of refraction, , where and are the angle of incidence (optics), angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices and . The refractive indices also determine the amount of light that is reflectivity, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle. The refractive index, n, can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Focal Plane
In optics, a conjugate plane or conjugate focal plane of a given plane ''P'', is the plane ''P′'' such that points on ''P'' are imaged on ''P′''. If an object is moved to the point occupied by its image, then the moved object's new image will appear at the point where the object originated. In other words, the object and its image are interchangeable. This comes from the principle of reversibility which states light rays will travel along the originating path if the light's direction is reversed. Depending on how an optical system is designed, there can be multiple planes that are conjugate to a specific plane (e.g. intermediate and final image planes for an object plane). The points that span conjugate planes are called conjugate points. For a thin lens or a curved mirror, + = , where is the distance from the object to the center of the lens or mirror, is the distance from the lens or mirror to the image, and is the focal length of the lens or mirror. Interchanging the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Focus (optics)
In geometrical optics, a focus, also called an image point, is a point where ray (optics), light rays originating from a point on the object vergence (optics), converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the circle of confusion, blur circle. This non-ideal focusing may be caused by optical aberration, aberrations of the imaging optics. Even in the absence of aberrations, the smallest possible blur circle is the Airy disc caused by diffraction from the optical system's aperture; diffraction is the ultimate limit to the light focusing ability of any optical system. Aberrations tend to worsen as the aperture diameter increases, while the Airy circle is smallest for large apertures. An image, or image point or region, is in focus if light from object points is converged almost as much as possible in the image, and defocus aberration, out of focus if light is not well converged. The border between these is sometimes define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
