Gladstone-Dale formula

The refractive index of a solid can be estimated via the Gladstone-Dale formula. It is especially useful for complex oxides, for which the Gladstone-Dale formula can be written ... 

Estimate the refractive indices of the ceramics barium titanate, BaTiOg, and lead tita-nate, PbTi03, using the Gladstone - Dale formula. Densities are as follows BaTi03, 6017 kgm PbTi03, 8230 kg m. ... 

The refractive index of a (transparent) fluid is a function of the fluid density. The relationship is exactly described by the Clausius-Mosotti equation for gases, this equation reduces to a simple, linear relationship between the refractive index, n, and the gas density, p, known as the Gladstone-Dale formula. Therefore, refractive index variations occur in a fluid flow in which the density changes, for example, because of compressibility (high-speed aerodynamics or gas dynamics), heat release (convective heat transfer, combustion), or differences in concentration (mixing of fluids with different indices of refraction). 

It is common knowledge that, aecording to the empirieal Gladstone-Dale formula and the theoretically proven Lorentz-Lorenz formula, the refractive index of optical material is proportional to its density. However, despite density decrease in the range of doses R < 6.0... 

Table 10.5 shows a comparison between calculated and observed values for a series of solid amorphous polymers. Remarkable is the fact that the very simple formula of Vogel (1948-1954), Rv = nM, gives about the same standard deviation as the more complex and theoretically better explicable formulas of Lorentz-Lorenz and Gladstone-Dale. 

Make up a solution of potassium chloride in water (say 10 per cent, by weight), and determine the refractive index first of pure water, and then of the solution, for the D line at a temperature of about 20 The density, of the solution relatively to that of water at 20 equal to i must also be determined at the same temperature. From the refractive indices obtained, calculate the specific and molecular refractivity of potassium chloride. Use the Gladstone and Dale formula. 

Using the formula by Ber-Gladstone-Dale for the refractive index... 

An attempt was made to compare the character of experimentally found change in the refractive index during PP chlorination with theoretical calculations based on simultaneous existence of the two types of structural chains mentioned above. For this purpose, the Lorentz-Lorenz theoretically derived formula and Gladstone-Dale and Fogel... 

The refractive index of molten sodium for light of wave-length 589fifi is 0 0045. J. Kanonnikoff 34 has calculated the refractive indices Rc for the C-line, and for infinity, the theoretical limit of the spectrum, Rx, according to Gladstone and Dale s formula ... 

M. le Blanc gave the refractive indices of solii. of potassium and rubidium bromides as 1 5593 and 1 5533 respectively, when the densities are 2"738 and 3 314 respectively. Hence the refraction eq. of potassium bromide by Gladstone and Dale s formula is therefore 24 32 and by Lorentz and Lorenz s formula 14-05 the corresponding values for rubidium bromide are27"62 and 15"98. The mol. refractions of potassium bromide in soln. by the two formulae are respectively 25"11 and 14 70 and of rubidium bromide in soln., 27 85 and 16 33. The mol. refractions of these salts are therefore greater in soln. than in the solid form. Crystals of potassium bromide, says H. Marbuch, exhibit optical activity. A. S. Newcomer found that sodium chloride was the only salt relatively soluble and yet capable of emitting fluorescent rays in the mid-ultra-violet region of the spectrum under the influence of X-rays. 

Applying the well known formula of Lorentz-Lorenz one finds a less good agreement. This formula is based on a theory which does not account for the influence of the internal field. The Gladstone and Dale equation is a purely empirical relation which seems to cover the actual behaviour of systems of this kind very satisfactorily. 

Landolt made a careful study of the formula proposed by J. H. Gladstone and J. Dale for the molecular refractivity of organic compounds. He investigated the time-reaction between iodic and sulphurous acids leading to the liberation of iodine, collaborated with Richard Bornstein, professor of physics in the Agricultural Institute, Berlin, in compiling the valuable Physikalisch-chemische Tabellen (1883 and later eds.), and did much work on the practical applications of optical activity and polarimetry. ... 

Refractivity of Substances in Solution.—In the case of not too strong solutions, the refractivity of the solute can be determined (with fair approximation, at least ) from the values of the refractivity of the solution and of the solvent, according to the ordinary mixture formula. Let i, and be the refractive indices of the solute, solvent, and solution respectively, and if, 4, 4 the corresponding densities then, if the solution contains p per cent, of the solute, we obtain (using the R formula (Gladstone and Dale))—... 

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