Unlike uniaxial minerals, biaxial crystals have 2 optic axes.
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The main difference between biaxial and axial crystals is that biaxial crystals have two optic axes.
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A surprising system of intersecting Cherenkov rings in a biaxial crystal at precisely defined particle energies was predicted.
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However these two special directions are generally not of particular interest; biaxial crystals are rather specified by their three refractive indices corresponding to the three axes of symmetry.
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The most remarkable result of this work is the prediction that a single ray of light entering a biaxial crystal at a certain angle would emerge as a hollow cone of rays.
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Armed with this insight and his new formulation of the problem, he derived, for the first time, a closed expression for the Cherenkov output in a biaxial crystal in terms of elliptic functions.
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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 " ?, " n " ? and " n " ?.
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Few would dispute the verdict of James David Forbes, an editor of the eighth edition of the " Encyclop�dia Britannica " : " His scientific glory is different in kind from that of Young and Fresnel; but the discoverer of the law of polarization of biaxial crystals, of optical mineralogy, and of double refraction by compression, will always occupy a foremost rank in the intellectual history of the age . " In addition to the various works of Brewster already mentioned, the following may be added : " Notes and Introduction to Carlyle's translation of Legendre's Elements of Geometry " ( 1824 ); " Treatise on Optics " ( 1831 );"
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