Land 4500 MKII Premier, Operation And Maintenance Manual

Page: 88 / 139

Model 4500 Premier Dust and Opacity Monitor
88
C1-2 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
-acL
I
o
where:
τ
= Transmittance
I
o
= Intensity of light into the medium (see 1 below)
I = Intensity of light out of the medium (see 3 below)
a = Attenuation Coefficient
c = Concentration of Pollutant
L = Distance light beam travels through the medium (see 2 below)
1
2
3
Since opacity (Op) = 1 -
τ
, the above equation becomes:
(1 - Op) = e -acL or Op = 1 - e -acL
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
= -acL/2.303
c = k x OD where k = -2.303
aL
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.