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A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. [1]
A finite ray or real ray is a ray that is traced without making the paraxial approximation. [12] [13] A parabasal ray is a ray that propagates close to some defined "base ray" rather than the optical axis. [14] This is more appropriate than the paraxial model in systems that lack symmetry about the optical axis.
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. [1] If the space is two-dimensional, then a half-space is called a half-plane (open or closed). [2] [3] A half-space in a one-dimensional space is called a half-line [4] or ray.
In topology, a curve is defined by a function from an interval of the real numbers to another space. [49] In differential geometry, the same definition is used, but the defining function is required to be differentiable. [53] Algebraic geometry studies algebraic curves, which are defined as algebraic varieties of dimension one. [54]
In Euclidean geometry two rays with a common endpoint form an angle. [14] The definition of a ray depends upon the notion of betweenness for points on a line. It follows that rays exist only for geometries for which this notion exists, typically Euclidean geometry or affine geometry over an ordered field.
Half-line (geometry) or ray, half of a line split at an initial point Directed half-line or ray, half of a directed or oriented line split at an initial point; Ray (graph theory), an infinite sequence of vertices such that each vertex appears at most once in the sequence and each two consecutive vertices in the sequence are the two endpoints of an edge in the graph
The result is a linear system of three equations, which can be solved by Gaussian elimination or Cramer's rule, for example. An alternative way uses the inscribed angle theorem for parabolas. In the following, the angle of two lines will be measured by the difference of the slopes of the line with respect to the directrix of the parabola.
In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the concept of caustics in geometric optics . The ray's source may be a point (called the radiant) or parallel rays from a point at infinity, in which case a direction vector of the rays must be specified.