( ampe? orient Fy F.c8 Vana C deli iatth, 2. a theory leads to rather complex expressions involving infinite series of terms where the series converges more and more slowly as the ratio of the diameter of the spherical particle to the wave length of radiation increases. For spheres of any size the Mie general equations are as follows, given by Sinclair (5): - he oS ��pen > a f=1 (hee (_An = (a n Pn) eer = e_-7- +i ) sc Equation 6 Where A and P ere complex functions of gf and m. — m = index of refraction of particles h = scattering coefficient \ For transparent (non-ebsorbing) spheres, m is real and Equation 6 yields the total amount of light thet is taken out of the incident beam. For absorbing particles m is comflex and equation 6 ylelda only that part of the light which is scattered by the spherical particle, For absorbing spherical particles the total amount of light abstracted from the beam (scattered and absorbed) is given by ni = 2B. 277 ( REAL ( ( (174 (4,+P,) a . an#] a} ) ) = - Equation 7 ) - Where ’ h' = extinction coefficient (scatter and absorbtion coefficient). "REAL" stands for the real part of the expression in brackets, Houghton (7) has shown thet for a given wave length of light Mie's Equation may be reduced to the following: — Is Ip exp( <][x Da re kg )------- Equation 8 - Where Kg = total area cross-section as calculated by Lowen and Houghton and others, Ky is given as a function of, where a Even for the relatively simple case under consideration (diélectric spheres) the computational problem of Mie's equations is formid- able, Lowan (9) has computed Mie's Equations ford= 0.5 to a= 6.0. H. G. Houghton (7) has calculated the total scattering from non-absorbing water drops whose index of refraction is 4/3 for values of X= 6.0 tonk= 24, A study of Mie's equations shows that for particles larger than air molecules the scattering coefficient does not follow such a simple law as the inverse fourth - power of the wave length as indicated by Rayleigh (Eqns. 1 and 2), —- T0048 83] =.