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If the absorptivity varies over the frequency spread of the beam, the more strongly absorbed frequencies will be depleted, and the absorptivity will therefore decrease with sample path length. Chemical and physical interactions in the sample may modify the nature of the absorbing species, causing the absorptivity to vary with concentration. Thus it is necessary to check each sample to determine whether Beer's law is obeyed before attempting a quantitative analysis. 



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The absorptivity is defined as the fraction of the energy incident on a body that is absorbed by the body. The incident radiation depends on the radiative conditions at the source of the incident energy. The spectral distribution of the incident radiation is independent of the temperature or physical nature of the absorbing surface unless radiation emitted from the surface is partially reflected back to the surface. Compared with emissivity, the absorptivity has additional complexities because directional and spectral characteristics of the incident radiation must be included. It is desirable to have relations between emissivity and absorptivity so that measured values of one will allow the other to be calculated.


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Absorbance A is directly proportional to the path length l and the concentration of the absorbing species c. That is 
A ∝ cl
A = acl
where a is a proportionality constant called the absorptivity. When the concentration is expressed in moles/litre and the path length in centimeters, the absorptivity is called the molar absorptivity or molar extinction coefficient ε.

Thus, A = εcl
$\log$ $\frac{I_{0}}{I}$ = $\varepsilon\ cl$

Absorptivity Coefficient

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Absorptivity and absorption coefficient are not the same. In the first place, the former is dimensionless whereas the latter has the dimensions of inverse length, which itself ought to signal caution. More to the point, the connection between them is sometimes tenuous at best. Consider, for example, radiation incident on bodies sufficiently thick that transmission by them is negligible. We now can attach a more precise meaning to "sufficiently thick": much thicker than the absorption length at the wavelength of the radiation. With this assumption, the absorptivity of the body is 1 minus its reflectivity. How does the reflectivity of the body depend on its absorption coefficient? For many materials over many wavelength intervals, reflectivity changes hardly at all even with huge increases in absorption coefficient. And if there is a change, it is likely to result in a decrease in absorptivity. For example, the absorption coefficient of metals such as silver and aluminum is usually huge compared with that of insulators such as quartz and salt, a million times or more, especially at visible and near visible wavelengths. And yet reflectivities of metals are high, and hence their absorptivities are lower than those of insulators. Finally, there is this important distinction to be kept in mind: absoptivity is a property of a body whereas absorption coefficient is a property of a material.  

Molar Absorptivity

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The molar absorption coefficient, molar extinction coefficient, or molar absorptivity, is a measurement of how strongly a chemical species absorbs light at a given wavelength. It is an intrinsic property of the species; the actual absorbance, A, of a sample is dependent on the pathlength l and the concentration c of the species via the Beer- Lambert law, A= εcl

Absorptivity of Black Body

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A black body surface completely absorbs external irradiation, regardless of direction and wavelength distribution. Its surface absorptivity is always 1. The reflectivity of a black body is always zero. The monochromatic absorptivity of a real body surface is less than 1 for external irradiation, thus its reflaction ratio is not zero relative to direction and wavelength. By comparison, the radiation and absorption of real bodies differ from those of black bodies, but all basic laws of thermal radiation are based on the black body- thus, in order to calculate and analyze the radiation heat transfer of real bodies, certain secondary factors must be neglected accordingly. 
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