Relative refractive index

Fraunhofer rules do not include the influence of refraction, reflection, polarization and other optical effects. Early Iziser particle analyzers used Fraunhofer approximations because the computers of that time could not handle the storage cuid memory requirements of the Mie method. For example, it has been found that the Fraunhofer-based instrumentation cannot be used to measure the particle size of a suspension of lactose (R.I. = 1.533) in iso-octane (R.I. = 1.391) because the relative refractive index is 1.10, i.e.- 1.533/1.391. This is due to the fact that diffraction of light passing through the particles is nearly the same as that passing around the particles, creating a combined interference pattern which is not indicative of the true... 

In many cases, only the relative refractive index change is of interest and the range of refractive index variation is small so the phase shift is less than 2n. In this case, the phase ambiguity issue can be avoided. The relative refractive index change can be calculated based on the spectral shift of the interferogram. 

In these expressions x is the size parameter and m is the relative refractive index, defined by... 

If mx = m2, then An = B = 0 and the coefficients (8.2) reduce to those for a homogeneous sphere. We also have ima 0An = lima >0 = 0 therefore, in the limit of zero core radius the coefficients (8.2) reduce to those for a homogeneous sphere of radius b and relative refractive index m2, as required. When m2= 1, the coefficients reduce to those for a sphere of radius a and relative refractive index mx this gives us yet another check on the correctness of our solution. 

If m, the average relative refractive index, varies only slightly over the frequency region of interest, then the circular dichroism (CD) spectrum 0(co) and the optical rotatory dispersion (ORD) spectrum < >([Pg.193]

SUBROUTINE BHCYL CALCULATES AMPLITUDE SCATTERING MATRIX ELEMENTS AND EFFICIENCIES FOR EXTINCTION AND SCATTERING FOR A GIVEN SIZE PARAMETER AND RELATIVE REFRACTIVE INDEX THE INCIDENT LIGHT IS NORMAL TO THE CYLINDER AXIS PAR .ELECTRIC FIELD PARALLEL TO CYLINDER AXIS PERIELECTRIC FIELD PERPENDICULAR TO CYLINDER AXIS sc sc sc scsc scsc sc sc sc sc ... 

The magnitude of the aberration is proportional to h2, but it decreases as n2, the square of the relative refractive index. Once again, it is apparent that a small refractive index is beneficial. 

The following table shows the angular location of the green bands in the HOTS of various size spheres of relative refractive index 1.46 ... 

The consequences of Mie s theory for absorption (i.e., for tinting strength) are now considered. Calculations from Mie s theory, using the relative refractive index n and the absorption index k, are given in Figure 8 [1.30]. The parameter a on the abscissa can once more be taken as a relative measure of the particle size. The following conclusions may be drawn ... 

The lowest curve applies to pigments with a small absorption index k and high relative refractive index n, as is usually the case with inorganic pigments (e.g., red iron oxide). Here, there is a distinct maximum [1.11], [1.16]. 

Consider first a series of eight views of the same data matrix for the intensity coefficient ii for a relative refractive index m of 1.200. Figures 1 through 8 represent different perspective viewpoints of the same three-dimensional matrix viewed from the front, right-hand side, back, etc., so as to reveal details of the simple behavior of complicated mathematical functions. 

The exact electromagnetic scattering theory of the concentric shell model was first solved by Aden and Kerker (1.) and shortly thereafter by Guttler (2). The problem has been extensively studied both theoretically and experimentally for aerosols by Kerker and co-workers and is reviewed in Kerker s book (3 ). The aerosol system had a core of relative refractive index m =2.105 and a shell of m2=1.482 corresponding to silver chloride coated with linolenic acid. The results indicated that for a smooth variation in the refractive index of the shell, the refractive index might not be sensitive to the form of the variation. 

The typical results of the wide-angle light-scattering (WALS) analysis on the latex particles that were presumed to be cores are given in Table I where the theoretical model to be fitted was either S = sphere or CS = core-shell, the variance measured the goodness of fit, the modal size parameter is given by aM = 27rr/A, aQ is the log normal breadth parameter, DM is the core diameter in ym, mi the relative refractive index of the core and m2 the relative refractive index of the shell of indicated thickness. 

Independent of the model used, it is quite clear that the core diameter is 0.44 to 0.45 ym and the relative refractive index of the core is 1.22+0.02. The evidence for a shell structure is again very tenuous. The "shell" thickness is unrealistically large, constant in extent, and little different from the results for the no-acid latex. If a shell structure was present it was at best marginally observable in the wide-angle light scattering. 

Inversion of WALS data gave evidence for a uniform sphere, independent of pH. At best, only marginal evidence for a shell of low relative refractive index and ill-defined extent was obtained. 

The radius of the spherical particle is r, and the relative refractive index, n, is the ratio (npln0) of the refractive index for the particle (np) to that of the suspending media (nc). As seen in Figure 11.1, particles with higher refractive indices scatter light more efficiently. The refractive index of polystyrene beads (1.6), generally used... 

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