Editing Absorbance (section)

=== Beer-Lambert law ===
The roots of the term absorbance are in the [[Beer-Lambert law#Beer–Lambert law|Beer–Lambert law]]. As light moves through a medium, it will become dimmer as it is being "extinguished". Bouguer recognized that this extinction (now often called attenuation) was not linear with distance traveled through the medium, but related by what we now refer to as an exponential function.

If <math>I_0</math> is the intensity of the light at the beginning of the travel and <math>I_d</math> is the intensity of the light detected after travel of a distance {{nowrap|<math>d</math>,}} the fraction transmitted, {{nowrap|<math>T</math>,}} is given by

<math display="block">T=\frac {I_d}{I_0} = \exp(-\mu d)\,,</math>

where <math>\mu</math> is called an [[Propagation constant#Attenuation constant|attenuation constant]] (a term used in various fields where a signal is transmitted though a medium) or coefficient. The amount of light transmitted is falling off exponentially with distance. Taking the natural logarithm in the above equation, we get

<math display="block">-\ln(T) = \ln \frac {I_0}{I_d} = \mu d\,.</math>

For scattering media, the constant is often divided into two parts,<ref>{{Cite book |last=Van de Hulst |first=H. C. |title=Light Scattering by Small Particles |publisher=John Wiley and Sons |year=1957 |isbn=9780486642284 |location=New York}}</ref> {{nowrap|<math>\mu = \mu_s + \mu_a </math>,}} separating it into a scattering coefficient <math>\mu _s</math> and an absorption coefficient {{nowrap|<math>\mu_a</math>,}} obtaining

<math display="block">-\ln(T) = \ln \frac {I_0}{I_s} = (\mu_s + \mu_a) d\,.</math>

If a size of a detector is very small compared to the distance traveled by the light, any light that is scattered by a particle, either in the forward or backward direction, will not strike the detector. (Bouguer was studying astronomical phenomena, so this condition was met.) In such case, a plot of <math>-\ln(T)</math> as a function of wavelength will yield a superposition of the effects of absorption and scatter. Because the absorption portion is more distinct and tends to ride on a background of the scatter portion, it is often used to identify and quantify the absorbing species. Consequently, this is often referred to as [[absorption spectroscopy]], and the plotted quantity is called "absorbance", symbolized as {{nowrap|<math>\Alpha</math>.}} Some disciplines by convention use decadic (base 10) absorbance rather than Napierian (natural) absorbance, resulting in: <math>\Alpha_{10} = \mu_{10}d </math> (with the subscript 10 usually not shown).