# double refraction wikipedia

n and The numerical difference between one RI value and the other RI value measured in any one case is called the "birefringence" for that test, and the difference between the highest possible RI and the lowest possible RI considering all possible directions is called the birefringence of the gemstone. = {\displaystyle {\vec {k}}\parallel {\vec {z}}} i c ⁡ is the rotation of polarization due to the coupling of the light with the magnetization. {\displaystyle {\vec {E_{i}}}={\begin{pmatrix}\cos \beta \\\sin \beta \\0\end{pmatrix}}e^{-i\omega (t-n_{1}z/c)}} / ⁡ i Following the notation of Hubert, the generalized dielectric cubic tensor t The other ray vibrates perpendicular to the vibration of the first ray and in a direction between perpendicular to and parallel to the optic axis (usually at some inclination) and so does not obey Snell's Law (i.e. (   → {\displaystyle Q} The magnetic field is decreasing leading to a coherent magnetization rotation from 1 to 2, At positive field, the magnetization switch brutally from 2 to 3 by nucleation and propagation of magnetic domains giving a first coercive field named here. r H ) r / We emphasized with the fact that it is because the light propagation vector is perpendicular to the magnetization plane that it is possible to see the Voigt effect. + ⁡ sin sin δ D {\displaystyle n_{\parallel }} δ {\displaystyle L} ω ) {\displaystyle \epsilon } is counted from the  crystallographic direction. is the induction defined from Maxwell's equations by 0 M It is defined as the bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. {\displaystyle \delta \beta } + This gives another coercive field named. This ray is named the ordinary ray (usually indicated with ω). The maximum RI difference between these two rays is named "birefringence", often indicated by the symbol "Δ" (Greek letter delta). When an anistropic stone is examined in the direction parallel to an optic axis, the stone will behave as an istropic gemstone. = {\displaystyle m_{i}^{2}} = ( {\displaystyle {\vec {E_{r}}}={\begin{pmatrix}E_{rx}\\E_{ry}\\0\end{pmatrix}}} s M t Therefore no doubling of facets will be seen in that direction either. Uniaxial stones (those crystallizing in the trigonal, hexagonal and tetragonal systems) will show two readings and have one optic axis. where ϕ represent the real and imaginary part of take the following form : where E D 0 the electric field and a homogenously in-plane magnetized sample μ 8, pp. {\displaystyle T<{\frac {T_{c}}{2}}} H ∥ + {\displaystyle B_{1}} sin the material refraction indices and When the two rays change their direction of travel (i.e. is proportional to The strength of birefringence (BI) varies with direction and we measure the maximum BI (Δ). e 0 and for ) and perpendicular → sin : When the magnetization is perpendicular to the propagation wavevector, on the contrary to the Kerr effect, is the difference of refraction indices depending of the Voigt parameter − ψ + in the same way with respect to the geometry in reflexion for the magnetization. A calcite crystal laid upon a paper with some letters showing double refraction Birefringent materials can give rise to colors when placed between crossed polarizers. are approximately twice of ) χ The aim is to calculate real. < / ϵ / {\displaystyle {\vec {m}}={\begin{pmatrix}\cos \phi \\\sin \phi \\0\end{pmatrix}}} In contrast to the common longitudinal/polar Kerr effect, the hysteresis cycle is even with respect to the magnetization, which is a signature of the Voigt effect. k are refracted) and move in different directions this phenomenon is called "double refraction. {\displaystyle B_{1}} ϕ . → or D ) ∥ {\displaystyle (\mu _{0}H)^{2}} {\displaystyle \beta }

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