and Huffman who also include a computer code for its computation) describes the
way in which the electromagnetic wave passes through the particle and thus requires
the setting of a refractive index, m ref . The theory uses a dimensionless parameter, the
size parameter, x, defined as
x ¼
2πa
λ
¼ k N a
ð4:25Þ
where a is the particle radius and λ is the wavelength which can be used to scale
results for identical particle size to wavelength ratios.
In Fig. 4.5, Mie theory results are shown for three values of x for m ref ¼ (1.60,
+0.01). The refractive index is complex and the imaginary part, m ref,i , plays a role in
the absorption by the particle. For the three cases, the curves have been normalized
such that the integral over the 4π solid angle is one.
m ref,i is related to the absorption coefficient by the equation
κ λ ¼
4πm ref ,i
λ
ð4:26Þ
and also we can relate this to the real (ε r ) and imaginary (ε i ) parts of the dielectric
constant using
ε r ¼ m
2
ref ,r À m
2
ref ,i
ð4:27Þ
and
Fig. 4.4 Scattering regimes
identified in a plot of particle
radius against the
wavelength of the incident
light. Visible wavelengths
are identified to the top left
4.2 Scattering of Light by Dust
289