sin éAéAw where T is a transmissivity (in general, a product of various transmissivities and reflectivities obtained from the Fresnel coefficients discussed in Sec. 7.2). For our purposes here all we need to know about T is that it is finite and nonzero and hence can be ignored.
Because of the azimuthal symmetry of a sphere, Aw = Aw,, whereas é is a different function of é,, or conversely, for every splinter. In the limit Aé ^ 0 Eq. (8.62) becomes
where we omit T. This can be written more compactly by way of the impact parameter b = a sin é- :
The differential scattering cross section is an infinite series of terms of the form of Eq. (8.63) or Eq. (8.64). Singularities, or caustics, in the differential scattering cross section occur at scattering angles for which ddi cos di sin §i
or, equivalently, db b ,
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