# Beer

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## 1. The classical law and its history

When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium. Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width $L$ of the medium, as suggested diagrammatically in Figure 1.One may conjecture that, at any illuminated plane $x$ within the medium, the decrease in the intensity $I$ of the radiation with distance would be proportional to the uniform concentration $c$ of the absorber and to the local intensity of the light at that point; that is

$\frac{\mathrm d}{\mathrm d x} ( I(x) )=-\alpha cI(x) (1)$

where $\alpha$ is a proportionality constant. Integration of this equation leads to

$\ln\frac{I(0)}{I(x)}=\alpha c x$

whence, on choosing $x$ to be the exit plane for the radiation, and with $\varepsilon=\alpha ln(10)=2.303\alpha$:

$\log_{10}\frac{I(0)}{I(L)}=\varepsilon c L$