Optical depth, or optical thickness, is a measure of transparency. Optical depth is defined by the negative natural logarithm of the fraction of radiation (e.g., light) that is not scattered or absorbed on a path. Hence optical depth is dimensionless, and particularly is not expressed in units of length; however the optical depth to an object will typically approach zero as the spatial distance to the object decreases.

The optical depth expresses the quantity of light removed from a beam by scattering or absorption during its path through a medium. If Failed to parse (Missing texvc executable; please see math/README to configure.): I_0

is the observed intensity after a given path, then optical depth Failed to parse (Missing texvc executable; please see math/README to configure.): \tau

following equation:

In atomic physics, the optical depth of a cloud of atoms can be calculated from the quantum mechanical properties of the atoms. It is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): \tau = \frac{d^2 \nu N} {2 c \hbar \epsilon_0 A \gamma},