Average index of refraction

Another potential effect is if one species affects the concentration of others due to chemical interactions. If the concentration of a species that is hygroscopic changes, the water content and average index of refraction for the particle may change simultaneously. For example, a reduction of about 7% in the index of refraction due to increased hydration can lead to a change in the scattering efficiency of as much as 34% (Hegg et al., 1993). 

Although there is no doubt that the particle extinction method is superior to classical reflection/transmission techniques for determining the effective complex index of refraction of coal, it is more suitable for spherical particles rather than irregularly shaped particles. For coal and char particles, it is very likely that material and shape nonhomogeneity will affect the results obtained in experiments. Therefore, the particle extinction technique can be used to obtain average index of refraction data for coal particles. 

In the case of a multicomponent particle, the index of refraction m reflects the mixture of species in the particle and can be approximated by the volume average of the indices of refraction of the individual components. Doing so assumes implicitly that the particle is a homogeneous mixture. This is not quite accurate if the particle, in fact, contains a core of one type of material surrounded by a shell of another. Previous studies have shown, however, that the error in refractive index incurred by the homogenous particle assumption, as compared with a calculation of refractive index that explicitly accounts for an insoluble core, is less that 20% (Sloane 1983 Larson et al. 1988). The volume-average index of refraction m for an aerosol containing n components is calculated from... 

If the index of refraction of a thin material were modulated in Heu of its absorption, the resultant transmittance function for a gra ting prepared as in the absorption case is given by equation 9 where n is the average index of the thin film. An is the amphtude of the index perturbation, and T is the thickness of the film. 

K represents the following constant parameters n is the index of refraction of the liquid, X is the laser wavelength in air, and 0 is the angle at which the scattering intensity is measured. For polydisperse samples, the autocorrelation function plot is the sum of exponentials for each size range. Once the average translational diffusion coefficient of the sample is determined, the equivalent spherical diameter can be determined by using the Stokes-Einstein... 

When characterizing particulate matter of unknown composition, it is necessary to assume a value for the index of refraction to infer the diameter from a measured intensity ratio. This causes inherent uncertainties in any reported size distribution unless all particles are of a known and uniform composition. In the case of automobile exhaust particles, the composition is certainly unknown and would probably include some combination of carbon particles and lead halides condensed on nuclei. Figure 1 is indicative of expected variations from such a spread of particle compositions. In the range of low a, the characteristic curve for nonabsorbing particles oscillates around an average value which is approximately the n = 1.57 — 0.56i data. Thus the intensity ratio curve for the absorbing soot is a convenient one to assume as the calibration standard for automobile exhaust particulates. Here this assumption results in a maximum error of approximately 30% when measuring particles of unknown composition. 

In contrast to the present treatment there are two types of earlier theories of refraction of light. Yvon32 has developed a statistical-mechanical theory of the refractive index. This theory is set up in such a way that an explicit expression is obtained for the index of refraction. It does not, however, contain an analysis of the optical phenomena (such as the extinction of the incident field) which are involved. These last aspects are considered very carefully in the other, electrodynamic, type of theory, which Hoek,8 following work done by a number of authors, has presented with great rigor. The disadvantage of this second method is that macroscopic quantities are not obtained by statistical-mechanical methods, but by averaging the microscopic quantities oVer physically infinitesimal volume elements. The result is that almost all the effect of density fluctuations is lost. Both of the theories mentioned assume furthermore thp molecular polarizability to be a constant independent of intermolecular distances. 

On the other hand, if n is the index of refraction of the medium, the solution of the homogeneous equation is the average field E. Indeed if Eq. V.ll is averaged over all microscopic configurations, the first term vanishes, because of relation (Eq. IV 29) between the average polarization and the average field, so that the average... 

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