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Huygens principle of double refraction, named after Dutch physicist Christiaan Huygens, explains the phenomenon of double refraction observed in uniaxial anisotropic material such as calcite. When unpolarized light propagates in such materials (along a direction different from the optical axis ), it splits into two different rays, known as ...
The principle yields an equivalent problem for a radiation problem by introducing an imaginary closed surface and fictitious surface current densities. It is an extension of Huygens–Fresnel principle, which describes each point on a wavefront as a spherical wave source.
The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. [1] The sum of these spherical wavelets forms a new wavefront.
Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution ("spheroid") but is described by three unequal principle refractive indices n α, n β and n γ. Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid is a spheroid).
Following his remarks on the propagation medium and the speed of light, Huygens gives a geometric illustration of the wavefront, the foundation of what became known as Huygens’ Principle. His principle of propagation is a demonstration of how a wave of light (or rather a pulse) emanating from a point also results in smaller wavelets: [12]
Notation for calculating the wave amplitude at point P 1 from a spherical point source at P 0.. At the heart of Fresnel's wave theory is the Huygens–Fresnel principle, which states that every unobstructed point of a wavefront becomes the source of a secondary spherical wavelet and that the amplitude of the optical field E at a point on the screen is given by the superposition of all those ...
Thus Huygens' construction and Fermat's principle are geometrically equivalent. [19] [Note 6] Through this equivalence, Fermat's principle sustains Huygens' construction and thence all the conclusions that Huygens was able to draw from that construction. In short, "The laws of geometrical optics may be derived from Fermat's principle". [20]
The Huygens–Fresnel principle is one such model; it states that each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point.