Refraction, double

In the discussion of the piezoelectric effect in Chapter 6 the tensor character of the permittivity of a dielectric was recognized although attention was focused on the piezoelectric coefficients. Because the optical and electro-optical properties of dielectrics are determined by their refractive indices or, equivalently, by their permittivities (see Eq. (2.120)), it is now necessary to consider these parameters in some detail. 

In an isotropic dielectric such as a normal glass, the induced electrical polarization is always parallel to the applied electric field and therefore the susceptibility is a scalar. In general this is not the case in anisotropic dielectrics when the polarization depends on both the direction and magnitude of the applied field. The three components of the polarization are written 

In an anisotropic dielectric the phase velocity of an electromagnetic wave generally depends on both its polarization and its direction of propagation. The solutions to Maxwell s electromagnetic wave equations for a plane wave show that it is the vectors D and H which are perpendicular to the wave propagation direction and that, in general, the direction of energy flow does not coincide with this. 

Crystals may have two optic axes, not necessarily perpendicular, in which case they are termed biaxial. Orthorhombic, monoclinic and triclinic crystals are biaxial hexagonal, tetragonal and trigonal crystals are uniaxial cubic crystals are isotropic. In the following discussion attention is confined to uniaxial crystals. 

Those rays, e.g. SO, for which the electric displacement component of the wave vibrates at right angles to the principal section (indicated by the dots) travel at a constant speed irrespective of direction they are the ordinary or o rays. 

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When the sample is capable of exhibiting double refraction, the specimen will then appear bright against a dark background. For example, when a uniaxial crystal is placed with the unique c axis horizontal on the stage, it will be alternately dark and bright as the stage is rotated. Furthermore, the crystal will... 

In the theory of optics this phenomenon is accounted for in terms of geometrical construction, but the physical picture is less convincing. Double refraction is a well-documented property of most crystals, at its most spectacular in Iceland spar. The double image of an object viewed through the crystal indicates the existence of two independent rays and not the components of a single ray. In mathematical terms the two rays are linearly independent and therefore orthogonal. Any intermediate situation represents a linear combination of the two orthogonal basis vectors and can be resolved into two components. What happens to an individual photon is however, not clear. 

Double-pulse ruby laser, 14 697-698 Double refraction, 14 675 Double salts, lanthanide, 14 633-634 Double-stranded DNA viruses, 3 135... 

Birefringence (or double refraction) is the decomposition of a light ray into two rays when it passes through certain types of crystalline material. This occurs only when the material is anisotropic, that is, the material has different characteristics in different directions. Amylose and amylopectin polymers are organized into a radially anisotropic, semicrystalline unit in the starch granule. This radial anisotropy is responsible for the distinctive... 

Because of the double refraction of the crystallites, the crystalline iPP phase appears bright under the microscope with crossed polarizers, the amorphous phase, however, appears black. If the iPP/PS film is molten (> 170 °C) and then briefly isothermally tempered at 130-135 °C,i.e., below the melting point of iPRthe growth of typical spheru-lite crystal structures can be observed under the microscope. 

In frequency regions where absorption is small the two indices of refraction , and n2 give rise to the phenomenon of double refraction. One of the most common uses for this property is in making wave retarders such as quarter-wave plates incident light linearly polarized with equal x and y field components is phase shifted upon transmission because of the two different phase velocities c/w, and c/n2. An entire field, usually referred to as crystal optics, arises out of this and further applications of crystal anisotropy. 

In interference microscopy the illumination is split into two beams [1,2]. The beam splitter is a half-silvered mirror. In reflection, one beam is reflected from the sample, while the other is reflected from a flat reference mirror [20-22]. Transmission is more complex as the beam splitter may be a double refracting crystal, and the two beams can be displaced horizontally or vertically [20-22], In all cases the two beams are recombined so that they interfere. The interference pattern can be used to measure the specimen thickness in transmission or the specimen roughness in reflection. 

Physical properties of solid polyphosphate glasses and their melts are also in accord with the conclusions drawn from chemical studies. The X-ray diffraction pattern shows the polyphosphate anions to consist of long chains of P04 tetrahedra (32) and the same conclusion is reached by studying the double refraction of fibers formed by rapidly drawing supercooled melts of Graham s salt (101). 

According to H. Lose, the dry crystals are not deliquescent J. J. Berzelius says they are. The crystals have a negative double refraction. Ammonium hydrofluoride volatilizes completely when heated. According to H. Rose, when ammonium hydrolluoride is mixed with silica or a silicate and calcined, the silicate is more readily decomposed than if hydrofluoric acid had been used. On electrolysis with a current of 5 amperes, 0. Ruff and E. Geisel9 obtained fluorine. 

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