LambertBeerGesetz

Lambert-Beer Gesetz, commonly known as the Beer-Lambert law, is a fundamental relation in analytical spectroscopy that describes how the intensity of light diminishes as it traverses an absorbing medium. The law connects the absorbance of a solution to its concentration and the optical path length.

Mathematically, absorbance A = ε c l, where ε is the molar absorptivity (a material- and wavelength-dependent constant with units L mol^-1 cm^-1), c is the solute concentration in mol/L, and l is the path length of the light through the sample in cm. Transmittance T = I / I0 = 10^{-ε c l}. For natural logarithms, I = I0 e^{-α c l}, with α related to ε by α = ε ln 10. The relationship is approximately linear for dilute, non-scattering solutions at a given wavelength.

History and naming: the law is attributed to Johann Heinrich Lambert (for the attenuation with thickness) and to August Beer (for the dependence on concentration); in many contexts it is referred to as the Beer-Lambert or Lambert-Beer law. Some formulations also credit Bouguer and others; the combined name Lambert-Beer-Bouguer is used in physics and chemistry texts.

Applications and limitations: the law underpins quantitative spectrophotometry, enabling concentration measurements from absorbance in chemistry, biochemistry, environmental science, and medicine. Limitations include deviations at high concentrations due to molecular interactions, scattering by particulates, fluorescence, instrumental stray light, and non-monochromatic light. The law assumes a homogeneous, non-scattering medium and a single dominant absorbing species at the chosen wavelength.