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The term “optical thickness” is ambiguous, as two totally different definitions occur in the literature:
The optical thickness of a light-absorbing medium is its geometrical thickness times its intensity attenuation coefficient.
For example, an optical thickness of 1 implies that the transmitted power is reduced to 1/e (≈ 37%) of its original value.
This definition is often used e.g. in atmospheric optics.
It is larger than the optical density by the factor ln 10 ∼ 2.303.
The optical thickness of a transparent medium is sometimes understood to be the same as the optical path length, which is its geometric thickness multiplied by the refractive index.
This is the quantity which determines the phase delay for light passing through the medium and is therefore relevant e.g. in interferometers.