The intensity change by absorption in a volume is proportional to

I 0 (λ)	the initial monochromatic radiance [W·m-2·m-1·sr-1];
dL	the light path [m];
n	the number density of the absorber [molec m-3];
σa(λ)	is the absorption cross-section at wavelength λ [m-2].

n·σ_a is the absorption coefficient, k_a [m^-1].

Integration along the light path leads to the Beer-Lambert Law:

For a homogeneous atmosphere this can be rewritten as

The integrated absorption component in the Beer-Lambert equation

is called opacity or optical depth, τ.

The transmissivity t(s) can then be derived as

The absorptivity a(s) can then be derived as

t(L) + a(L) = 1

a(s) = 1 - t(s)

For an opacity τ → ∞ the absorptivity a → 1. This is called the optically 'thick' case.

Note that σ_a, τ, t and a are functions of the wavelength λ.