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Light absorption

When light passes through a medium, some of the photons may interact with the matter (atoms, molecules, clusters etc.) and be absorbed (their energy being transformed in internal energy). As a result, the intensity decreases as light passes through the absorbing medium.

We find that the variation ‘dI’ of the light intensity ‘I’ crossing a very thin slice ‘dx’ of the absorbing medium is proportional to the incoming intensity and the thickness of the thin slice ‘dx’, i.e. each thin slice absorbs a given portion of the incoming light. The proportionality factor ‘k(n)’ depends both on the frequency of the incoming light and on the nature of the matter.

Lambert Beer law


Aborption cell

If we assume ‘k’ to be 0.9, 90% of the incoming light will pass through a slice of unity thickness and 10% will be absorbed.
If we assume a homogenous medium, a uniform layer for example, we can easily integrate the linear first order differential equation. The solution is of the form:

Lambert Beer Equation

Where I0 is the initial intensity at ‘x=0’. This relation ship is known as Lambert-Beer’s law first described by Pierre Bouguer in the early 18th century. Check .wikipedia or britannica.com for more information on PierreBouguer
For a non-uniform absorbing layer we obtain:Absorption Equation

The optical depth or optical thickness ‘t‘ of a specific light path through a medium with absorption coefficient ‘k(n,x)’ and thickness ‘L’ is defined as the integral of the absorption coefficient over the entire light path. Despite its name, the optical depth is dimensionless. Values for ‘t‘ larger than one indicate strong absorption.

optical depth equation

When considering absorption of light in the discharge cell, the absorption is obviously due to the interaction between the photons and the different plasma species. We are mainly concerned by the interaction between the photons and the atoms or ions. The absorption coefficient depends therefore on the “atomic absorption probability” (proportional to the Einstein coefficient) and the density of the absorbing species, e.g. atoms in an electronic state able to interact with the photon. Light emitted by the plasma species in the discharge may be re-absorbed by the same species at different places in the discharge. This effect is known as self-absorption.
As the distribution of atoms and ions in the discharge cell is not homogeneous, the absorption coefficient varies within the discharge volume.
A well known example for the use of light absorption in analytical chemistry is Atomic Absorption Spectroscopy (AAS), using for example a flame or an electrothermal atomiser.


First published on the web: 09. 01. 2008.

Author: Thomas Nelis. The text extends topics presented by Prof. E.B Steers during the first GLADNET Training course held in Antwerp, Be, in September 2007.