Quantitative infrared spectroscopy - the Lambert-Beer law

When infrared radiation passes through a sample of any substance the intensity is reduced by the same factor for each equal increase in distance travelled. The intensity thus decays exponentially and, if the decay is due only to absorption, rather than to scattering and absorption, then 

The infrared-absorption spectrum of a substance is ideally a plot of the transmittance or the absorbance of a suitable thickness against the wavelength or wavenumber of the infrared radiation. In practice the losses of intensity by reflection at the surfaces of a sample can often be neglected and then, from equations (2.5) and (2.6) 

If the sample is very thick the transmittance will approach zero and the absorbance will tend to infinity for all wavelengths. In order to avoid too high an absorbance for a solid polymer it is usually necessary to work with samples of thickness between about 30 and 300 pm. 

All modern spectrometers are computer-controlled and are not only capable of producing their output in the form of absorbance or transmittance spectra plotted on a chart but also permit other forms of display and various kinds of mathematical processing of the data. A simple example of such processing is the ability to add together scaled versions of the absorbance spectra of two or more substances to find a match with the spectrum of a mixture of the substances and so determine the eomposition of the mixture, provided that interactions in the mixture do not change the individual spectra. 

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