A calcite crystal laid upon a paper with some letters showing the double refraction
Birefringence, or double refraction, is the division of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcitecrystals, depending on the polarization of the light. This is explained by assigning two different refractive indices to the material for different polarizations. The birefringence is quantified by:
Δn = ne _ no
where no is the refractive index for the ordinary ray and ne is the refractive index for the extraordinary ray.
More generally, an anisotropic dielectric material has a dielectric constant that is a rank_2 tensor (3 by 3 matrix). A birefringent material corresponds to the special cases of a real-symmetric dielectric tensor ε with eigenvalues of no², no², and ne² along the three orthogonal principle axes of polarization. (Or, sometimes, only two axes are considered, corresponding to a single propagation direction.)
Cellophane paper is a cheap birefringent material.
In principle, birefringence could also arise in magnetic, not dielectric, materials, but substantial variations in magnetic permeability are rare at optical frequencies.
Birefringent materials are used widely in optics to produce polarizingprisms and retarder plates such as the quarter-wave plate.
Its birefringence is extremely large, with indices of refraction for the o- and e-rays of 1.6584 and 1.4864 respectively.
The property called birefringence has to do with anisotropy in the binding forces between the atoms forming a crystal, so it can be visualized as the atoms having stronger "springs" holding them together in some crystalline directions.
Birefringence is formally defined as the double refraction of light in a transparent, molecularly ordered material, which is manifested by the existence of orientation-dependent differences in refractive index.
In contrast, birefringence refers to the physical origin of the separation, which is the existence of a variation in refractive index that is sensitive to direction in a geometrically ordered material.
The maximum brightness for the birefringent material is observed when the long (optical) axis of the crystal is oriented at a 45 degree angle with respect to both the polarizer and analyzer, as illustrated in Figure 8(c).
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