Principle Fermat s

The equivalent of the grating equation for a prism is the application of Fermat s principle to the configuration shown in Fig. 12. 

Use Lagrange s method of multipliers to derive the law of refraction of light from Fermat s principle of least time between two fixed points. 

To develop a system of mechanics from here without the introduction of any other concepts, apart from energy, some general principle that predicts the course of a mechanical change is required. This could be like the Maupertuis principle of least action or Fermat s principle of least time. It means that the actual path of the change will have an extreme value e.g. minimum) of either action or time, compared to all other possible paths. Based on considerations like these Hamilton formulated the principle that the action integral... 

Following Atkins [68], the propagation of particles follows a path dictated by Newton s laws, equivalent to Hamilton s principle, that particles select paths between two points such that the action associated with the path is a minimum. Therefore, Fermat s principle for light propagation is Hamilton s principle for particles. The formal definition of action is an integral identical in structure with the phase length in physical optics. Therefore, particles are associated with wave motion, the wave-particle dualism. Hamilton s principle of least... 

Not only mechanics but all of physics can be derived from the principle of least action. There are appropriate Lagrangian functions for electrodynamics, quantum mechanics, hydrodynamics, etc., which all allow us to derive the basic equations of the respective discipline from the principle of least action. In this sense, the principle of least action is the most powerful economy principle known in physics since it is sufficient to know the principle of least action, and the rest can be derived. Nature as a whole seems to be organized according to this principle. The principle of least action can be found under various names in nearly every branch of science. For instance the principle of least cost in economy or Fermat s principle of least time in optics. 

However, we can calculate the variation of the traveltime using Fermat s principle, which states that the traveltime is stationary with respect to a variation of the raypath L(r, Vj) ... 

Note that this equation has been obtained using Fermat s principle in which the result of a raypath perturbation is set equal to zero. Elquation (15.148) can be considered the linearization of the nonlinear equation (15.146). 

Fermat s principle - The law that a ray of light traversing one or more media will follow a path which minimizes the time required to pass between two given points. 

Not long after the formulation of Snell s law, the French mathematician Pierre de Fermat unified the laws of reflection and refraction by showing that both could be deduced from the hypotheses that light travels a path of least time. In other words, given two points A and B in a region with mirrors or with different media, the path of a ray of light from point A to point B will be that for which the time of travel is least. The implication of Fermat s principle is that light travels at a finite speed. ... 

Concave diffraction gratings were first introduced The concave diffraction grating is an optical element in spectrometric practice by Henry Rowland in 1883. combining two functions (1) reflecting and focusing Based on Fermat s principle, Rowland was able to... 

Fermat s principle The path followed by light (or other waves) passing through any collection of media from one specified point to another, is that path for which the time of travel is least. 

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