Transmittance

This article is about transmission through a medium. For transmission or refraction through an interface (between two homogeneous media), see Fresnel equations.

Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a cuvette of width l.

Earth's atmospheric transmittance.

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 (or other electromagnetic radiation) at a specified wavelength that passes through a sample. A related term is absorptance, or absorption factor, which is the fraction of radiation absorbed by a sample at a specified wavelength. Occasionally one also hears the terms visible transmittance (VT) and visible absorptance (VA), which are the respective fractions for the spectrum of light visible radiation. In equation form,

$\mathcal{T}_\lambda = {I\over I_{0}} \qquad \mathcal{A}_\lambda = \frac{I_0-I}{I_0}$

where $I_0$ is the intensity of the incident radiation and I is the intensity of the radiation coming out of the sample and $\mathcal{T}_\lambda$ and $\mathcal{A}_\lambda$ are transmittance and absorptance 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.

For liquids, transmittance is related to absorbance A (not to be confused with absorptance) as

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

In the case of gases it is customary to use natural logarithms instead, making absorbance A for gases

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

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

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

where $\alpha$ is the attenuation coefficient and $x$ is the path length. For liquids e is replaced by 10.

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

See also

• Opacity (optics)