Particle extinction coefficient (${\beta }_{\mathrm{ext}}=\int Q_{\mathrm{ext}}(r)\pi r^{2}n(r)dr$)

The total extinction cross-section per unit volume of particles is a length-inverse coefficient. Its path integral is optical depth. It combines scattering and absorption and differs from the dimensionless imaginary part of a complex refractive index. For liquid droplets with size-independent $Q_{\mathrm{ext}}$, ${\beta }_{\mathrm{ext}}=3Q_{\mathrm{ext}}w/(4{\rho }_w{r}_e)$.