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Mie theory describes the way in which spherical, homogeneous particles interact
with electromagnetic radiation. Certain assumptions are made about these
particles in order to simplify the situation. These assumptions are:
1) Only the interactions of a single particle with light of arbitrary
wavelength are considered.
2) The optical properties of the particle are completely described by
frequencydependent optical constants (i.e. the complex refractive index or the
complex dielectric function).
3) Scattering is elastic, i.e. the frequency of the scattered light is
identical to that of the incident light.
4) Only singlescattering occurs. That is, each individual particle
is acted on by an external field (due to the incident radiation) in isolation
from the other particles. The total scattered field is merely the sum of the
fields scattered by each particle (i.e. the particles do not affect each
other).
5) For a collection of particles, the number of particles is large and their
separations are random, so that the waves scattered by the individual particles
have no systematic phase relation.
6) The medium in which the particles are embedded is considered to be: a)
linear, b) homogeneous and c) isotropic.
The theory used to find the transmission spectra of small particles from the optical constants is known as Mie Theory. This calculates the Qfactors, which are the efficiency factors for extinction, scattering and absorption. There is no simple explicit formula for the Qfactors, however if 2a / , (where a is the radius of a spherical particle and is the wavelength of the incident light), then for a spherical particle:
where n = n  ik (Bohren & Huffman 1983).
Given the close relation between the complex refractive index and the complex dielectric function, we can also write these equations in terms of the dielectric function:
where epsilon =

i.
There are computer programs that use Mie Theory to evaluate the Qfactors and
thus produce the relevant spectra. These programs require the input of:
1) A dimensionless length 2 8a /
2) The real and imaginary parts of the refractive index of the materials
n() = n  ik,
or the real and imaginary parts of the dielectric function of the material
epsilon =

i.
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