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In studying geometry one concentrates on the position of points and on the length, orientation and curvature of lines. Geometrical–optical illusions then relate in the first instance to object characteristics as defined by geometry.
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays:
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
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.
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).
Similar to Euclid's much more famous work on geometry, Elements, Optics begins with a small number of definitions and postulates, which are then used to prove, by deductive reasoning, a body of geometric propositions about vision. The postulates in Optics are: Let it be assumed That rectilinear rays proceeding from the eye diverge indefinitely;
A meridional ray is a ray that passes through the axis of an optical fiber. A skew ray is a ray that travels in a non-planar zig-zag path and never crosses the axis of an optical fiber. A guided ray, bound ray, or trapped ray is a ray in a multi-mode optical fiber, which is confined by the core.
The geometry of classical optics is equivalent no matter which direction light is considered to move because light is modeled by its path, not as a moving object. However, his theory of clarity of vision (the circular appearance of far rectangular objects) makes sense only if the ray emits from eyes.