When light is absorbed in a homogeneous medium with a certain absorption coefficient α, the optical intensity decays exponentially in proportion to exp(−α 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.
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