Mipnynx 1pnynx

with the prime superscript denoting a first derivative with respect to the argument of a function, x = kr and y = mx, r is the radius of the particle, m its refractive index. In the above Mie solution, the medium surrounding the scattering particle was taken to be vacuum (m=1), however, if the surrounding medium has a real refractive index m2 (no absorption), then we obtain the solution by replacing m by m/m2 and A (in vacuum) by X/m2. Also

sin 0

In the above, P^ (cos 0) is the associated Legendre polynomial, ^n and are the Ricatti-Bessel functions that are related to the Bessel functions through

where jn(z) an(i hn (z) are the spherical Bessel functions, while Jn^i(z) and (2)

are the fractional-order Bessel functions, and 2 is a complex number. The scattering function for forward scattering can be computed from

1 00

We can define a dimensionless efficiency factor for extinction by Qext = ^ext/nr2, and similarly for scattering and absorption. We can then compute Qext from

and the corresponding efficiency factor for scattering from

We can compute, for example, the scattering cross-section for a distribution of particle sizes from 