Editing Transmittance (section)

=== Beer–Lambert law ===
{{main|Beer–Lambert law}}

The [[Beer–Lambert law]] states that, for ''N'' attenuating species in the material sample,
:<math>\tau = \sum_{i = 1}^N \tau_i = \sum_{i = 1}^N \sigma_i \int_0^\ell n_i(z)\,\mathrm{d}z,</math>
:<math>A = \sum_{i = 1}^N A_i = \sum_{i = 1}^N \varepsilon_i \int_0^\ell c_i(z)\,\mathrm{d}z,</math>
where
*''σ''<sub>''i''</sub> is the [[Cross section (physics)|attenuation cross section]] of the attenuating species ''i'' in the material sample;
*''n''<sub>''i''</sub> is the [[number density]] of the attenuating species ''i'' in the material sample;
*''ε''<sub>''i''</sub> is the [[molar attenuation coefficient]] of the attenuating species ''i'' in the material sample;
*''c''<sub>''i''</sub> is the [[amount concentration]] of the attenuating species ''i'' in the material sample;
*''ℓ'' is the path length of the beam of light through the material sample.

Attenuation cross section and molar attenuation coefficient are related by
:<math>\varepsilon_i = \frac{\mathrm{N_A}}{\ln{10}}\,\sigma_i,</math>
and number density and amount concentration by
:<math>c_i = \frac{n_i}{\mathrm{N_A}},</math>
where N<sub>A</sub> is the [[Avogadro constant]].

In case of ''uniform'' attenuation, these relations become<ref name=GoldBook2>{{GoldBookRef|title=Beer–Lambert law|file=B00626|accessdate=2015-03-15}}</ref>
:<math>\tau = \sum_{i = 1}^N \sigma_i n_i\ell,</math>
:<math>A = \sum_{i = 1}^N \varepsilon_i c_i\ell.</math>

Cases of ''non-uniform'' attenuation occur in [[atmospheric science]] applications and [[radiation shielding]] theory for instance.