What is the reason for the variation of absorption in a linear fashion, and that of transmittance in a non linear fashion?

01 January 1970 1 7K Report

Why does the absorbance vary in a linear fashion, whereas the transmittance varies in an exponential fashion?

Can this be explained mathematically/intuitively or are these results based on experimentation?

Actually, absorbance changes neither linearly with length of the lightpath nor with concentration, just in a first approximation, which becomes exact, absurd as it may sound, in the limit of vanishing absorption. The reason why transmittance decays approximately exponentially is that the decrease of intensity is proportional to the intensity itself. Why only approximately? For details see this review: Article The Bouguer-Beer-Lambert Law: Shining Light on the Obscure

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