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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 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.
For calcite, if we interchange the equatorial and polar radii of Huygens's oblate spheroid while preserving the polar direction, we obtain a prolate spheroid touching the sphere at the equator. A plane through the center/origin cuts this prolate spheroid in an ellipse whose major and minor semi-axes give the magnitudes of the extraordinary and ...
This causes an additional shift in that beam, even when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate slightly around that of the ordinary ray, which remains fixed. [verification needed]
It is an extension of Huygens–Fresnel principle, which describes each point on a wavefront as a spherical wave source. The equivalence of the imaginary surface currents are enforced by the uniqueness theorem in electromagnetism , which dictates that a unique solution can be determined by fixing a boundary condition on a system.
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 ...
Examples of the application of Huygens–Fresnel principle can be found in the articles on diffraction and Fraunhofer diffraction. More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect the interaction of light ...
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]