Beer- Lambert's statement

Lambert’s Beer law is a theory that relates the attenuation of light (amount of light absorbed) passing through a certain material to the properties of this material.

Thus, the Lambert’s Beer theory can be defined as the linear relationship between light absorbance and concentration of the absorbing material.

So the Lambert’s Beer law can be written as

$$A=ε∗L∗c$A=\epsilon \ast L\ast c$

where A is the light absorbance (how much light is absorbed by the material) so it can be defined as the relation between incident light intensity and resulted light intensity given by A=log(Io/I)$A=log(Io/I)$

ε$$(pronounced as epsilon) is the absorption coefficient which is wavelength dependent

L is the path length of the incident light through the material

C is the concentration of the absorbing material

So by knowing the intensity of the incident light and calculating the output light intensity, absorbance could be then calculated and consequently the concentration of the absorbing material could be determined.

The Lambert’s Beer law can find many applications especially in the biomedical field.

However, the traditional Lambert’s Beer law is not fully applicable when dealing with materials with very high densities and concentrations (i.e highly scattering mediums), the reason behind this is that light tends to travel extra distances inside the material due to the absorption and scattering effects of the material, as a result the intensity of the output light is significantly attenuated. However, these effects are taken into account in the modified Lambert’s Beer law.

Modified Lambert’s Beer law

The modified Lambert’s Beer has 2 extra factors from the traditional law which accounts for the extra path length of the light and the attenuation factor.

$$A=ε∗L∗DPF∗c+G$A=\epsilon \ast L\ast DPF\ast c+G$

where DPF is the differential path length factor which accounts for the extra distances traveled inside the substance

G is the attenuation factor