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In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry , projective geometry has a different setting, projective space , and a selective set of basic geometric concepts.
Mandelbrot set with 12 encirclements. Zooming into the boundary of the Mandelbrot set. In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in ...
The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow.
These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation: n 1 n 2 = v 2 v 1 = λ 2 λ 1 = ϵ 1 μ 1 ϵ 2 μ 2 {\displaystyle {\frac {n_{1}}{n_{2}}}={\frac {v_{2}}{v_{1}}}={\frac {\lambda _{2}}{\lambda _{1}}}={\sqrt {\frac {\epsilon _{1}\mu _{1 ...
Prism (optics) An optical prism is a transparent optical element with flat, polished surfaces that are designed to refract light. At least one surface must be angled — elements with two parallel surfaces are not prisms. The most familiar type of optical prism is the triangular prism, which has a triangular base and rectangular sides.
Distortion (optics) In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image. It is a form of optical aberration .
Thus a prism of 1 Δ would produce 1 cm visible displacement at 100 cm, or 1 meter. This can be represented mathematically as: where is the amount of prism correction in prism dioptres, and is the angle of deviation of the light. For a prism with apex angle and refractive index , .
Geometrical optics. 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:
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. [1] These optically anisotropic materials are described as birefringent or birefractive.
The simplest compound prism is a doublet, consisting of two elements in contact, as shown in the figure at right. A ray of light passing through the prism is refracted at the first air-glass interface, again at the interface between the two glasses, and a final time at the exiting glass-air interface. The deviation angle of the ray is given by ...