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.
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:
Where I0 is the initial intensity at x=0. This relation ship is known as Lambert-Beers 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:
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.
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
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.