Principal refractive index

If necessary, each refractive index is determined specifically through successive immersion in liquids of various refractive index until one is found where the sample disappears—knowing the refractive index of the liquid, one then knows the refractive index in a particular orientation. There may be one, two, or three principal refractive indices. 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

Identification of crystals under the microscope. Of the characteristics which are most useful for identification purposes the most readily determined are shape and refractive indices, The determinative method which has proved most valuable for microscopic crystals (such as those in the average experimental or industrial product) is to measure the principal refractive indices (up to three in number, depending on the symmetry of the crystal) and, if possible, to find the orientation of the principal opticafdirections with respect to the geometrical form of the crystal. This information, which can all be obtained by simple and rapid microscopio methods, is usually sufficient to identify any crystalline substances whose properties have previously been recorded. Mixtures of two or more crystalline substances can be identified by the same method in phase equilibrium studies and in industrial research it is not uncommon to encounter mixtures of three or four constituents, all of which can be identified in this way. 

The principal refractive indices of uniaxial crystals are usually symbolized w or nw for the more important of the two, the one which is constant for all orientations, and t or n for the other one. When e is less than w (as in monammonium phosphate) the crystal is described as uniaxial negative when e is greater than co, as in quartz, Si02 (co = 1 544, e = 1 553), the crystal is described as uniaxial positive. 

If three of these quantities are known, the fourth can be calculated. Thus, when it is possible to measure all three principal refractive indices, the measurement of the optic axial angle is, strictly speaking, superfluous. But in some eases it may be possible to measure only two of... 

Dispersion. The principal refractive indices of a crystal vary in magnitude with the frequency of light and in crystals of monoclinic or triclinic symmetry, the vibration directions of the principal indices may vary with frequency. Such variation is known as dispersion. 

Crushing has been recommended as a primary method because it is safe and will lead to the determination of the principal refractive indices of any crystalline substance, provided a sufficient number of randomly oriented fragments is observed it is a beginner s method. But the more experienced worker may often dispense with it, when the crystals being examined have a well-defined polyhedral shape. If the relation between crystal shape and optical properties is properly understood, it is possible to determine the principal indices by a limited number of observations on crystals selected because they lie in such positions that they necessarily show their principal indices. 

Crystals which appear to possess one twofold axis, or one plane of symmetry, or both (the twofold axis b being normal to the plane of symmetry) are probably monoclinic if so, crystals lying with their presumed b axes parallel to the microscope slide will show extinction parallel to this b axis, and the refractive index for this vibration direction is one of the principal refractive indices. The other two principal indices will be shown by crystals lying with their b axes along the line of vision for this aspect of the crystal, extinction is not parallel to a principal edge or to the bisector of edge angles, f... 

Crystals which appear to possess only a centre of symmetry or no symmetry at all are probably triclinic, and will probably not show their principal refractive indices when lying on their faces such crystals should be crushed. 

Zachariasen rounded off this work by calculating the three principal refractive indices of the crystal on the basis of his structure, accepting Bragg s theory (1924). The calculated values are close to the known indices of the crystal. 

Flow birefringence of polymer solutions is, in general, measured with the aid of an apparatus of the Couette type, containing two coaxial cylinders. One of these cylinders is rotated at constant speed, the other is kept in a fixed position. The light beam for the birefringence measurement is directed through the annular gap between these cylinders, in a direction parallel with the axis of the apparatus. In this way, the difference of principal refractive indices An is measured just in the above defined plane of flow (1—2 plane). 

If we try to understand the transmission of light waves in biaxial crystals, we start from the concept of the indicatrix, and to attempt to visualize what shape this must have to show the variation of refractive index with vibration direction for such crystals. From our previous knowledge of the indicatrix for uniaxial crystals, an ellipsoid of revolution with two principal refractive indices, n0 and ne, it is a simple step to see that the indicatrix for biaxial crystals will be a triaxial ellipsoid with three principal refractive indices, n7, np and na. 

Those rays, e.g. SE, for which the electric displacement component lies in the principal section travel at a speed which depends on direction they are the extraordinary or e rays. The refractive index ne for an e ray propagating along SX is one of the two principal refractive indices of a uniaxial crystal the other, n0, refers to the o rays. 

Recently, Heiberg et al. [26] have studied polarizabilities of the intermolecular contacts in bis(ethylenedithiolo)tetrathiafulvalene (BEDT-TTF) and bis(ethylenedioxy)tetrathiafulvalene (BEDO-TTF) molecular crystals by polarizing microscope techniques. The principal refractive indices and the corresponding optical axes have been calculated by tensorial addition of the bond polarizabilities of all bonds in the molecules. Comparison of calculated and measured values of the relative polarizabilities showed that the polarizabilities of the molecules only cannot yield the measured indicatrix and axes angle. Thus polarizabilities with other orientations must be involved. From the crystal structure of the molecular crystals it is known that 10 and four different contacts exist between the molecules of BEDT-TTF and BEDO-TTF, respectively, with contact distances lower than van der Waals distances. Assigning of polarizabilities of these contacts can explain the measured behavior. 

P = 0, 7t/2, n, 3tc/2. .. These bands are related to the direction of the principal refractive indices. They move when the polarizer and analyser are rotated simultaneously and are called "isoclinic" fringes. 

If the crystal is biaxial, there are three principal refractive indices (a, /3, and 7, with a less than (3 less than 7). The optical indicatrix has... 

Biaxial crystals Crystals that have two directions along which there is no double refraction (two optic axes). Such biaxial crystals are either orthorhombic, monoclinic, or triclinic, and have three principal refractive indices. 

Uniaxial crystals Crystals that are characterized by having one (and only onej direction along which there is no double refraction (one optic axis). These crystals are tetragonal, hexagonal, or rhombohedral, and have two principal refractive indices. 

In addition to morphological assessments of crystals, optical microscopy can be used to measure their refractive indices. To identify the crystal, it is not necessary to measure the principal refractive indices simply measuring two that are unique and reproducible is sufficient. These are termed the key refractive indices that, according to these researches, are all that are needed to identify any particular compound. 

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