By definition, internal transmittance is related to optical depth and to absorbance as
where
*τ is the optical depth;
*A is the absorbance.
The Beer–Lambert law states that, for N attenuating species in the material sample,
or equivalently that
where
*σ is the attenuation cross section of the attenuating species i in the material sample;
*n is the number density of the attenuating species i in the material sample;
*ε is the molar attenuation coefficient of the attenuating species i in the material sample;
*c 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
and number density and amount concentration by
where N is the Avogadro constant.
In case of uniform attenuation, these relations become
or equivalently
Cases of non-uniform attenuation occur in atmospheric science applications and radiation shielding theory for instance.