How to use a spectrometer?

### Reminder: the Beer-Lambert’s law

We consider a medium of width L that absorbs light: it will generally be the content of a cuvette containing the solution subjected to spectrometric analysis. The intensity of the absorbed light (i.e. that is stopped) by this medium is proportional to the intensity of light that passes through it and proportional to the concentration of light-absorbing molecules. On a small medium width dx, the decrease in the light’s intensity dI can be written as: dI=-λCdx and as such, the light’s intensity after having passed through the width L, is worth:

$\large \int_{0}^{L} dI = ln \frac{I}{I_{0}} = -\lambda C\int_{0}^{L}dx = -\lambda CL$

This expression is always used by bringing up the decimal logarithms and the dependence to concentration. By writing ε=λln10, the expression becomes: $\large A = \log \frac {I_{0}}{I} = \varepsilon L C$ and is called the Beer-Lambert’s law.

In practice, the Beer-Lambert’s law allows to access the concentration C if ε, I, I0 and L are known, or to access ε epsilon if I,I0,L and C are known. The graph of ε (or of any physical quantity that is proportional to it, like A for example) as a function of wavelength makes up the UV-visible spectrum of the studied sample.

In every case, the spectrometer must measure I0 and I and compare them. Both measures are necessary, as it is not possible to build an instrument that would measure a determined luminous intensity I0.