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Absorption and Transmission

Beer-Lambert Law describes how light is attenuated as it passes through an absorbing medium. In its simplest form, the intensity of an incident beam of monochromatic radiation ( Io ) decreases exponentially according to

when it passes through an absorbing medium where the exponential term is proportional to the thickness of the medium (b) and the concentration (c) of the absorbing species. In its equivalent form

the proportionality constant is the molar absorptivity (if the concentration is expressed in Moles liter-1), also commonly called the extinction coefficient, and the product is the absorbance (Abs). Note that absorbance is a dimensionless number and is defined only with reference to a specific wavelength.

Beer-Lambert Law assumes that any light that is not absorbed is transmitted. In real life, when electromagnetic radiation impinges on an object, one of four things can happen. The incident energy can be absorbed, scattered, reflected, or transmitted. This is shown mathematically by the relationship

in which ( Io ) is the incident intensity. After rearranging,

and the terms on the right are called the absorptance, scatter, reflectance, and transmittance, respectively. In those cases where scatter and reflectance are negligible, the equation further simplifies to

where incident energy is either absorbed or transmitted. Under these conditions, Beer-Lambert Law is applicable. Just as transmittance represents the fraction of light transmitted at a given wavelength, absorptance is equal to the fraction of light absorbed at that wavelength. The relationship between absorptance and absorbance can be obtained by combining Eq. 2 and 5

Optical density and absorbance are often used interchangeably. However, optical density refers to how much energy is transmitted through a medium including losses from reflection and scatter. When working with a clear coat, it makes sense to talk in terms of a coating’s absorbance. However, when dealing with a pigmented ink, reference to optical density is more correct. Only in the limit where Beer-Lambert Law is applicable are the two truly equal.

To learn more about how the absorbance of a coating affects the ability to cure the coating, click here.