# Transmittance

Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a cuvette of width l.
File:Ruby transmittance.svg
Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the ruby laser.

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

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

where ${\displaystyle I_{0}}$ 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

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

or, using the natural logarithm

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

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

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

where ${\displaystyle \alpha }$ is the attenuation coefficient and ${\displaystyle x}$ 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.