Page 4
User Guide
Model 4200 Dust & Opacity Monitor
3.2 Beer-Lambert’s Law
The mathematical relationship between the light transmitted by a medium and
the quantity of pollutant present is known as the Beer-Lambert Law and may be
written;
τ
= I
= e
-ac
l
I
o
where:
τ
= Transmittance
Io =
Intensity of light into the medium (see 1 below)
I
=
Intensity of light out of the medium (see 2 below)
a
=
Attenuation Coefficient
c
=
Concentration of Pollutant
l
=
Distance light beam travels through the medium (see 3 below)
Fig. 3-1
Since opacity (Op) = 1 -
τ
, the above equation becomes:
(1 - Op) = e
-ac
l
or
Op = 1 - e
-ac
l
Note that the quantity c is the amount of dust in the optical path. Optical Density
(or extinction) is defined as:
OD = -log
10
τ
=
-ac
l
/2.303
or = k x OD
where k = -2.303/a
l
By comparing a series of optical density measurements with gravimetric dust
measurements taken at the same time, it is possible to determine the value of k.
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