When light is absorbed in a homogeneous medium with a certain absorption coefficient <$\alpha$>, the optical intensity decays exponentially in proportion to <$\exp(-\alpha z)$>, where <$z$> is the propagation distance. (It is assumed that the intensity is not affected by divergence or convergence of a beam.) One defines the absorption length as the inverse of the absorption coefficient. After that propagation length, the intensity decays to <$1/e$> (≈37%) of its initial value. After four absorption lengths, only ≈1.8% of the initial intensity is left.
The term penetration depth is often used with the same meaning as absorption length, but it should be considered as a more general term because limited penetration into a material may not only result from light absorption, but also from reflection. That is a typical situation for metals, for example, where the rapid decay of intensity is mostly due to reflection.
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