Beer-Lambert Law
It is quite intuitive that a higher concentration of the absorbing species in a sample would lead to higher absorption of the light. Furthermore, the higher thickness of the sample should result in higher absorption.
Consider a cell (also called cuvette) of length, l, containing a solution of an absorbing molecule. The absorbing species in the sample can be represented by discs of cross-sectional area, σ. Now, let us consider a slab of infinitesimal thickness, dx and area, A (Figure 4.4). If an incident radiation of the resonance frequency (the frequency that causes maximum transition) having intensity Io enters the sample cell, its intensity decreases as it penetrates the sample. Let us suppose that the intensity of the radiation before entering the infinitesimal slab is Ix.
Figure 4.4 A diagrammatic representation of light absorption by sample molecules in an infinitesimal thin slab within the sample
If the concentration of the absorbing molecules = 
, the fraction of the area occupied by the molecules in the slab = 
Therefore, the fraction of the photons 
absorbed is proportional to 
. Assuming the probability of absorption if a photon strikes the molecule to be unity,