The refractive index

TABLE 32.2 Refractive Indices of Some Glasses and Crystals  

The refractive index of Si02 glass can be raised by adding Ge02. This has important implications in the fabrication of optical fibers (Section 32.11). 

FIGURE 32.5 (a) Change in n with % for several commercial glasses. (Hydrogen F, Sodium D, and Hydrogen C refer to specific light sources that have % = 589, 486, and 656nm, respectively.) 

FIGURE 32.6 Dispersion as a function of wavelength for a number of ceramics. The inset is the classic illustration of dispersion, a prism separating white light into its spectral components. 

The use of scalar molar bond refractions for the calculation of refractive indices is described in section 9.2.3. This allows the refractive index of a randomly oriented sample to be calculated and also permits an understanding of the wide range of refractive indices that polymers can have, as shown in table 9.3. 

Polymers are not, however, always randomly oriented and the phenomenon of orientation is discussed in the next two chapters, chapters 10 and 11. One of the ways used to obtain information about the degree of orientation of the polymer is to measure either the refractive indices of the polymer for light polarised in different directions or its birefringences, i.e. the differences in refractive index for light polarised in different directions. In chapter 11 the theory of the method is described in terms of the polarisability of structural units of the polymer. This polarisability is a second-rank tensor like the molecular polarisability referred to in the earlier sections of this chapter and, insofar as the assumption of additivity in section 9.2.3 holds, it is in fact the sum of the polarisability tensors of all the bonds in the unit. Since, however, the whole basis of the method is that the structural units are anisotropic, the tensors must be added correctly, taking account of the relative orientations of the bonds, unlike the treatment used to calculate the refractive index of PVC in example 9.1, where scalar bond refractions are used. 

It is assumed that the orientation of every bond in the unit is known with respect to a set of axes 02 1 2X3 fixed in the unit and that the components of the bond polarisability with respect to axes fixed within each bond are also known. Equations (A.7) of the appendix are then used to refer the tensor components for each bond to 

OX 1X2X2 so that corresponding components for all bonds can be added. It is usual to assume that the polarisability tensor for a bond is cylindrically symmetric around the bond axis. This means (see the appendix) that, if the bond axis for a particular bond in the unit is chosen as the 0x3 axis of a set of axes OX1X2X2 the tensor takes the form an = a22 = oii and = a, with all other components zero, where at represents the component transverse to the bond and represents the component parallel to the bond. Values of at and ap are given for various types of bond in table 9.5. 

Let the bond make the polar and azimuthal angles 6 and 0 with respect to the axes OX1X2X2 of the unit and choose the Oxi axis so that it lies in the 0X1X2 plane. This can always be done because of the cylindrical symmetry of the tensor. The direction-cosine matrix linking the sets of axes OV1V2X3 and OX 1X2X2 is then 

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As in the case of density or specific gravity, the refractive index, n, for hydrocarbons varies in relation to their chemical structures. The value of n follows the order n paraffins < n naphthenes < n aromatics and it increases with molecular weight. 

As a consequence, other than its use in the ndM method, the refractive index is very often used in process operations because it can indicate smaii differences in product quality that would be missed by other measurements. The only restriction is that the color of the sample should be less than 5 on the ASTM D 1500 scale. 

The physics of X-ray refraction are analogous to the well known refraction of light by optical lenses and prisms, governed by Snell s law. The special feature is the deflection at very small angles of few minutes of arc, as the refractive index of X-rays in matter is nearly one. Due to the density differences at inner surfaces most of the incident X-rays are deflected [1]. As the scattered intensity of refraction is proportional to the specific surface of a sample, a reference standard gives a quantitative measure for analytical determinations. 

Nonetheless, the syimnetric interferometer remains very useful, because there, the wavelengdis of fringes with even cliromatic order, N, strongly depend on the refractive index, n, of the central layer, whereas fringes with odd cliromatic order are almost insensitive to This lucky combhiation allows one to measure the thickness as well as the refractive index of a layer between the mica surfaces independently and siniultaneously [49]. 

Figure Bl.26.13. Plot of versus K, the imaginary part of the refractive index.

Determination of the physical constants and the establishment of the purity of the compound. For a solid, the melting point is of great importance if recrystalhsation does not alter it, the compound may be regarded as pure. For a hquid, the boiling point is first determined if most of it distils over a narrow range (say, 1-2°), it is reasonably pure. (Constant boUing point mixtures, compare Section 1,4, are, however known.) The refractive index and the density, from which the molecular refractivity may be calculated, are also valuable constants for liquids. 

The density and the refractive index of a liquid will frequently be of value in assisting its characterisation. 

Refractive index. The refractive index of a liquid is conveniently determined with an Abbe refractometer. This refractometer possesses the following advantages ... 

The refractive index of a liquid is recorded as where t is the temperature at which the measurement is made, and D refers to the wave length of the D line of sodium. As already pointed out, it is usual to determine both the refractive index and the density of the liquid at 20° in any case they should be determined at the same temperatme. These two constants are useful in assisting the characterisation of a pure hquid they are particularly valuable for ahphatic hydrocarbons and similar compounds where the methods of characterisation by the formation of solid derivatives are not entirely satisfactory. 

Computed optical properties tend not to be extremely accurate for polymers. The optical absorption spectra (UV/VIS) must be computed from semiempiri-cal or ah initio calculations. Vibrational spectra (IR) can be computed with some molecular mechanics or orbital-based methods. The refractive index is most often calculated from a group additivity technique, with a correction for density. 

Note The ultimate result of the isomerization is a mixture of CH3CeCCH=CH2 and HCeCCH=CHCH3 (about 9 1). As the refractive index of these compounds is... 

Note 3. If after 15 min the refractive index has not increased considerably, 2 g of tert.-butylalcohol should be added. This may activate the base. 

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