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# Transmittance

In optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample.

$\mathcal{T} = {I\over I_{0}}$

where I0 is the intensity of the incident light and I is the intensity of the light coming out of the sample. The transmittance of a sample is sometimes given as a percentage.

Transmittance is related to absorbance A as

$A = - \log_{10}\mathcal{T}\ = - \log_{10}\left({I\over I_{0}}\right)$

or, using the natural logarithm

$A = - \ln\mathcal{T}\ = - \ln\left({I\over I_{0}}\right)$

From the above equation and the Beer-Lambert law, the transmittance is thus given by

$\mathcal{T} = e^{-\alpha \, x}$,

where α is the attenuation coefficient and x is the path length.

Note that the term "transmission" refers to the physical process of light passing through a sample, whereas transmittance refers to the mathematical quantity.