Beer’s law and beyond

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Beer’s Law and Beyond

Keith B. Oldham and J. Mark Parnis

Chemical Properties Research Group, Department of Chemistry, Trent University, Peterborough, Ontario, Canada.

Beer’s law describes the diminution of intensity as light traverses an absorbing medium.

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 diminishessteadily 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 planex within the medium, the decrease in the intensity I of the radiationwith distance would be proportional to the uniform concentration cof the absorber and to the local intensityof the light at that point; that is

A large clock tower and other buildings line a great river.

(1) where is a proportionality constant. Integration of this equation leads to (2) whence, on choosing x to be the exit plane for the radiation, and with