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Lambert-Beer Law

Inside an optek photometer, a precisely focused light beam is used to penetrate the process medium. A photoelectric silicon cell measures the resulting light intensity. The change in light intensity caused by light absorption and/or light scattering is described by the Lambert-Beer law.

Lambert Beer's law is a mathematical means of expressing how light is absorbed by matter. The law states that the amount of light emerging from a sample is diminished by three physical phenomena:
  1. The amount of absorbing material in its pathlength (concentration)
  2. The distance the light must travel through the sample (optical pathlength OPL)
  3. The probability that the photon of that particular wavelength will be absorbed by the material (absorptivity or extinction coefficient)
This relationship may be expressed as:

A = εdc
A = absorbance
ε = molar extinction coefficient
d = pathlength in cm
c = molar concentration


As a beam of light passes through an absorbing medium, the amount of light absorbed in any unit volume is proportional to the intensity of incident light times the absorption coefficient. Consequently, the intensity of an incident beam drops exponentially as it passes through the absorber. This relationship when expressed as Lambert's Law is:

T = 10-εcd or T = 10-A
T = transmittance
ε = molar extinction coefficient
c = molar concentration of the absorber
d = pathlength in cm

In a simplified approach, the transmittance can be expressed as the intensity of the incident radiation, Io which is ratioed to the light emerging from the sample, I. The ratio I/Io is referred to as transmittance or simply T.


Transmittance can be plotted against the concentration, but the relationship is not linear. The negative log 10 of the transmittance is, however, linear with the concentration.

Therefore, absorption is measured as:

A = -log10 (I/Io) or A = -log10 (T)