Rayleigh attenuation from refractivity ($L_{\mathrm{att}}=3N{\lambda }^4/[32{\pi }^3(n-1{)}^2]$)

In a dilute nonmagnetic medium of isotropic independent polarizable particles, $n-1\simeq N\alpha /(2{ϵ}_0)$ and the Rayleigh scattering cross-section is $8{\pi }^3{\alpha }^2/(3{ϵ}_0^2{\lambda }^4)$. Eliminating polarizability and setting direct-beam attenuation coefficient to $N\sigma$ gives the title relation. It describes scattering out of a narrow beam, not absorption of all radiant energy. It assumes fixed number density, negligible correlations/local-field corrections and a scalar polarizability; molecular anisotropy, aerosols and stratification require additional information.