Light as a Multifunctional Tool: Beer-Lambert Law
When light passes through matter, it is transmitted, absorbed,
or reflected. The relative absorption or reflection of light is used in several
monitoring devices to estimate the concentrations of dissolved substances, for example,
carbon dioxide in respiratory gas and hemoglobin in plasma. The field of absorption
spectrophotometry is based on the Beer-Lambert law, which states that if a known
intensity of light illuminates a chamber of known dimensions, the concentration of
the dissolved substance can be determined if the incident and transmitted light intensity
is measured:
It
= Ii
e−dCα
(10)
Solved for C,
C = 1/dα ln Ii
/It
(11)
where C is the concentration of the dissolved substance, d is the path length of
the light a, and α is an absorption constant for the substance C at the wavelength
used. Ii
and It
are the incident and transient light intensity,
respectively. The unknown concentration (C) is inversely proportional to the path
length (d) of light and directly proportional to the log of the ratio of incident
light to transmitted light intensity ( Fig.
30-32
). Red light and infrared light are generally used because the constituents
of interest to anesthesiologists (anesthetic agents, CO2
, hemoglobin)
absorb light in that range. It is also fortunate that red and infrared light can
penetrate tissue and may therefore be used to measure the concentration of hemoglobin
species in living tissue (see the section on
Figure 30-32
Cuvette. Light entering the cuvette is reflected and
absorbed. The concentration of substances absorbing and reflecting light can be
determined by measuring the amount of light entering and exiting the system.
pulse oximeters). Infrared light is absorbed by small molecules only if they have
bonds and are asymmetric. Therefore, nitrogen, oxygen, and helium cannot be measured
by infrared light. Another limitation of infrared light is that it is absorbed by
ordinary glass; therefore, the measurement chambers for these devices must be made
of sapphire, which is permeable to red and infrared light.
