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Reflection and transmittance for two dielectrics [permanent dead link ] – Mathematica interactive webpage that shows the relations between index of refraction and reflection. A self-contained first-principles derivation of the transmission and reflection probabilities from a multilayer with complex indices of refraction.
In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis
These equations can be proved through straightforward matrix multiplication and application of trigonometric identities, specifically the sum and difference identities. The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group.
In telecommunications and transmission line theory, the reflection coefficient is the ratio of the complex amplitude of the reflected wave to that of the incident wave. The voltage and current at any point along a transmission line can always be resolved into forward and reflected traveling waves given a specified reference impedance Z 0.
A time-domain reflectometer; an instrument used to locate the position of faults on lines from the time taken for a reflected wave to return from the discontinuity.. A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if ...
The second part introduces the definitions of reflection systems and reflection groups, the special case of dihedral groups, and root systems. [2] [3] Part III of the book concerns Coxeter complexes, and uses them as the basis for some group theory of reflection groups, including their length functions and parabolic subgroups.
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(A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation.