Invariance of the Spectrum of Light on Propagation

The question is raised as to whether the normalized spectrum of light remains unchanged on propagation through free space. It is shown that for sources of a certain class that includes the usual thermal sources, the normalized spectrum will, in general, depend on the location of the observation point unless the degree of spectral coherence of the light across the source obeys a certain scaling law. Possible implications of the analysis for astrophysics are mentioned.