Differentiation and Derivative Spectra

The differentiation of a curve or of its mathematical function is simply an estimation of the slope over the whole region. In the same way, it is possible to differentiate a spectrum (Fig. 2-3). In spectroscopy, the measured value is the ratio of the intensity of the 

The decrease in intensity of the light passing through a homogeneous transparent sample is not linear, as shown in Fig. 2-4. 

The relation between / and the concentration of either a dissolved sample, a transparent liquid, or a solid is given by Bougueur-Lambert-Beer law  

molar absorption, coefficient of absorbing species at wavelength A Tx transmittance at wavelength A. 

Usually the intensity /q is held constant over the entire range of wavelengths with an automatically controlled slit, automatic electronic adjustment of amplification, or automatic control of the voltage of the light source. 

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