First of all, let's introduce spectrophotometry.
Spectrophotometry is a method based on the selective absorption of electromagnetic radiation by substances with different molecular structures, which belongs to molecular absorption spectrum analysis. When light passes through the solution, the molecules of the measured substance absorb monochromatic light with a certain wavelength, and the intensity of the absorbed light is proportional to the distance through which the light passes. Although Bouguer had put forward the mathematical expression of the above relationship as early as 1729, it is generally believed that Lambert first discovered the expression in 1760, and its mathematical form is: T=I/I0=e-kb.
Where I0 is the incident light intensity, i is the transmitted light intensity, e is the base of natural logarithm, k is a constant, and b is the optical path length (usually expressed in cm).
Beer's law is equivalent to Bouguer's law, except that Beer's law is expressed by concentration. Combine these two laws to form Bill-Bouguer Law:
T=I/I0=e-kbc
Where c is the concentration of light-absorbing substance (usually in g/L or mg/L). After the logarithm of the above formula is based on 10, a linear expression is obtained:
a =-logT =-log(I/I0)= log(I0/I)=εBC
Where a is absorbance and ε is molar absorption coefficient or extinction coefficient.
The above expression is usually called Beer's Law. It shows that when monochromatic light with a specific wavelength passes through the solution, the absorbance of the sample is directly proportional to the concentration of absorbent in the solution and the distance through which the light passes.
When the wavelength, solution and temperature are determined, the molar extinction coefficient is determined by the characteristics of a given substance. In fact, the measured molar extinction coefficient is also related to the instrument used. Therefore, in quantitative analysis, the molar extinction coefficient of known substances is usually not used, but one or more substances with known concentrations are used to make calibration or working curves.