In optics and spectroscopy, transmittance is the fraction of incident light (electromagnetic radiation) at a specified wavelength that passes through a sample. The terms visible transmittance (VT) and visible absorptance (VA), which are the respective fractions for the spectrum of light visible radiation, are also used. The natural radiation of the cuvette corresponding to the temperature of the cuvette remains ignored - see radiative transfer equation.
In equation form,
where is the intensity of the incident radiation and is the intensity of the radiation coming out of the sample and and are transmittance and optical depth respectively. In these equations, scattering and reflection are considered to be close to zero or otherwise accounted for. The transmittance of a sample is sometimes given as a percentage.
Transmittance is related to optical depth τ (not to be confused with absorbance nor absorptance) as
If one want to express optical depth in decibels:
From the above equation the transmittance is thus given by
Note that the term "transmission" refers to the physical process of radiation passing through a sample, whereas transmittance refers to the mathematical quantity.
In plane geometry:
where, when the plane parallel assumption is invoked, with the angle of propagation of the ray from the normal of the surface.
In case of uniform attenuation optical depth is simply:
for example if there is a strong temperature or pressure nonuniformity in a material, the concentration is nonuniform but the cross section is uniform, so:
Another equation that can be useful in solving for is the following:
Where is a measure of absorbance. By manipulating the equation you can generate the more direct form of the equation:
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