Beer–Lambert law
Light or X-rays passing through a material fade exponentially with the distance travelled and how strongly the material absorbs.
The Beer–Lambert law describes how a beam of light, or other radiation, gets dimmer as it passes through something that absorbs it. Each thin slice of material removes the same fraction of whatever light reaches it, so the light fades exponentially, a process called attenuation. If one centimetre of a coloured liquid lets through half the light, two centimetres let through a quarter and three an eighth. The loss also grows with how concentrated the absorbing substance is and how strongly each molecule absorbs.
The idea was built up over more than a century. Pierre Bouguer found in 1729 that starlight fades exponentially with the length of its path through the atmosphere; Johann Heinrich Lambert stated the general rule in 1760; and August Beer showed in 1852 that coloured solutions behave the same way.
Chemists use the law constantly to measure concentrations: shine light through a sample, measure how much gets through and work out how much of a substance is present. Hospital laboratories measure substances in blood this way. The same logic explains X-ray images, where bone attenuates the beam far more than soft tissue, and why the Sun looks dimmer near the horizon, where its light crosses much more air.
The law works best for clear, dilute samples. It breaks down at very high concentrations and in cloudy materials that scatter light strongly.
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