Scattering, independent, from sphere

Figure 5.2 Plot of independent scattering intensities from spheres, thin disks, and thin rods.

Note that P is independent of particle size, as are the functional forms of /( (0) and ix (0) the absolute scattered irradiance depends on size (the volume squared), but it is difficult to measure absolute irradiances. Therefore, the radius of small spheres cannot readily be determined from scattering measurements in this sense, all small spheres are equal. 

Noctilucent cloud particles are now generally believed to be ice, although more by default—no serious competitor is still in the running—than because of direct evidence. The degree of linear polarization of visible light scattered by Rayleigh ellipsoids of ice is nearly independent of shape. This follows from (5.52) and (5.54) if the refractive index is 1.305, then P(90°) is 1.0 for spheres, 0.97 for prolate spheroids, and 0.94 for oblate spheroids. 

A different type of analysis has now provided this information (20) The dimension distributions p(a) of independent spherical scatterers with uniform density and diameter a which produces each of the terms in the sum in Equation (3) can be calculated (19) After obtaining the constants in the sum in Equation (3) by least-squares fits of this equation to the scattering curve measured for Beulah lignite at the University of North Dakota, we used these constants to evaluate the sum of the pore-dimension distribution functions for uniform spheres that are obtained (19) from the terms in the sum in Equation (3) The sum of these pore-dimension distributions was very similar to the power-law distribution given by Equation (4) The fact that we could obtain almost the same power-law dimension distribution by two independent methods suggests that such a distribution may be a good approximation to the pore-... 

In the case of electron diffraction, we consider the coherent, elastically scattered electrons only, so that the time-independent, static correlation function G(r, o) is obtained in terms of the number density Q(r) of atoms on the surface of a sphere a certain distance r from an atom at the origin ... 

As an example, consider a sphere of radius R with a black wall of temperature 4 flUed with an isothermal gas at 4, as shown in Figure 7.16. Neglect scattering and assume that the gas has a refractive index of 1 and an absorption coefficient k that is independent of the wavelength (gray assumption). The spectral intensity at the wall is a function of angle 0. From Equation (7.25), we have 4(0) = + 4 j(4)(1-c ). Since k is not a function of the wavelength,... 

Figure 5.19 Small-angle neutron scattering intensity obtained with a styrene-butadiene diblock copolymer having spherical butadiene microdomains. The peaks at very small q are due to a body-centered cubic lattice structure of ordered microdomains. The solid curve is the calculated intensity of independent scattering from solid spheres of mean radius 124 A. (From Bates etal.34)...

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