Beer-Lambert Law

A colored solution absorbs light because its dissolved particles intercept photons passing through. More particles in the way, or a longer path through the solution, means more chances for absorption. That is the whole intuition behind A = eps b c: absorbance A is directly proportional to molar absorptivity eps (how strongly that particular substance absorbs at a given wavelength, in /M/cm), path length b (in cm), and concentration c (in M). Double the concentration and you double the absorbance. Double the path length and you double it again. A darker blue solution absorbs more simply because it has more light-absorbing particles per unit volume.

Because A and c are directly proportional at fixed eps and b, a plot of absorbance versus concentration for several known standards gives a straight line through the origin, with slope eps times b. Make four or five standard solutions of known concentration, measure each absorbance on a spectrophotometer, and plot the points. Draw the best-fit line and find its slope. Then measure the absorbance of your unknown, and solve for its concentration using that same line: c = A divided by slope.

This connects directly to the idea of transmittance, the fraction of light that gets through. Absorbance is defined as the negative log base ten of transmittance, so it is the logarithmic cousin of percent transmitted light, not the same quantity. That log relationship is exactly why absorbance, not transmittance, is the one that scales linearly with concentration and makes calibration curves possible. Wavelength choice matters too: eps depends on wavelength, so the whole calibration setup assumes the instrument stays fixed at one wavelength throughout.