The equivalence theorem of light waves on scattering from a collection of particles is discussed. It is shown that when light waves are scattered from two different particulate media, the spectral density or the spectral degree of coherence may present identical distribution, provided that some relationship between the two particulate media is satisfied. An example of light waves on scattering from a collection of particles with random distribution is discussed, and the conditions for producing identical normalized spectral density and that for producing identical spectral degree of coherence are investigated. This phenomenon is illustrated with some numerical results.