Gladstone-Dale equation

A nice qualitative derivation of the Gladstone-Dale equation was given by Schoorl (1920). The Huygens-Fresnel wave optics leads to the conclusion that the refractive index is equal to the ratio of the light velocities in the two media of transmission and also to the ratio of the respective wave-lengths so Snellius law can be extended to... 

The required parameters in the calculation are Ushocked, t/s, and Wp. The shocked refi active index is given by the Gladstone-Dale equation nshocked=l+( -l)Pshocked/p, where p is the initial density of the PMMA (1.186 g/cm ) and n=1.487. Conservation of mass provides the shocked density pshocked=p/(l- Up / s) for a one-dimensional shock compression. Previous studies have validated the Gladstone-Dale model for shocked PMMA up to 22 GPa. [90-91]... 

For gases with n, 1, Eq. 16.39 can be simply reduced to the Gladstone-Dale equation ... 

Therein, n, V, N, a, and Rl respectively represent the refractive index, molecular volume, Avogadro s number, polarizability, and molecular refraction. The Gladstone-Dale equation is derived from Equation (18.1) when n is close to 1, as shown below [15]. 

It is found that a significant difference between the experiment and theoretical calculations occurs. Refractive indiees for the initial (non-chlorinated) PP film ealeulated by Lorentz-Lorenz and Gladstone-Dale equations equal n = 1.5200 and n = 1.5126, respectively. In accord with the experiment (Figure 22, curve 1), this eorresponds to ffl(Cl) = 54.6% and (C1) = 43%, respeetively. According to Fogel also, an underestimated refractive index is obtained for the initial film, with approximately the... 

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. 

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). 

The refractive index is usually estimated in terms the molar refraction R, which quantifies the intrinsic refractive power of the structural units of the material. Several definitions have been proposed for R. Two of these definitions incorporate both of the key physical factors determining the refractive index, and are thus especially useful. Equation 8.5 expresses n in terms of the molar refraction RT T according to Lorentz and Lorenz [1,2], and Equation 8.6 expresses n in terms of the molar refraction Rgd according to Gladstone and Dale [3]. 

This equation, which holds to a good approximation, represents nothing but the rule of Gladstone and Dale additively applied to the mixture For its verification the densities and the refractive indices of the components and those of the... 

According to the well known rule of Gladstone and Dale (cf. p. 576), variations in density within these series could be accounted for by the equations... 

Fig. 65 shows the course of the values of n,)q and ni)q in dependence on the water content a of the fibre, as found experimentally (dots), as calculated according to the additive rule of Gladstone and Dale (fully drawn lines), and as calculated according to equation (45) combined with equation (47)... 

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