Atmospheric Transmission Beer's Law

3/31/10Deviations from Beer’s LawreflectionI 0absorptionreflectiondirectdiffuse(scattered)Direct Beam:I(x) = I 0 exp(- β ext x)Transmission Coefficient for the DirectBeam:t direct = exp(- β ext x)xBeer’s Law applies to the directbeam onlyMass extinction coefficient• The extinction coefficient β e expresses extinction by reference to ageometric distance (or path length) through a medium• Problem: The measured transmission though a ink-water solution is 70%and the depth of the solution is 10 cm. Calculate β e .• What happens if the depth of the solution is doubled without addition of ink?• In remote sensing, we are usually interested in the mass of absorbingmaterial present, or the number of absorbing particles.• We define the mass extinction coefficient k e , relating the density of theabsorbing material (ρ) to β e :β e= ρk e€14