Aside from the math, there is a simple physical analog that helps explain this result. Consider diesel fumes belched from an exhaust pipe. Initially the fumes appear black, then gradually you are able to see through them without any trouble. This is not because the total scattering cross section of all the soot particles has changed, but because the soot has dispersed. If we consider a transparent cube of length "L" on a side, filled with soot, then the optical depth of this medium is inversely proportional to the square of "L", and therefore proportional to the areal density of soot particles: we can make it easier to see through the imaginary cube just by making the cube larger.