# Do the various frequencies of light within sunlight have the same coherence length?

I'm aware that the coherence length of sunlight can be observed with a Michelson-Morley interferometer. I haven't seen any experiment that separated the different colors within sunlight to determine if the coherence length varied with frequency.

My thoughts are that the sun is emitting bursts of electromagnetic radiation that vary in frequency, polarization, and phase. The only way I can see fringes forming is if a single burst is split by the mirrors producing two waves that are perfectly correlated in frequency, phase, and polarization. Once one arm of the interferometer is lengthened so that the two paths exceed the length of the EM bursts then fringes would be impossible. How could selecting specific frequencies cause the EM bursts to be correlated, especially in polarization?

The question is ill-defined because for visible light, the coherence length depends on the width of the interval via $$L_{\text{coherence length}} = \frac{2\ln 2}{\pi n} \frac{\lambda^2}{\Delta \lambda}$$ The spectral width $\Delta \lambda$ of the source is in the denominator. So the wider range of frequencies you include, the shorter coherence length you get. If you considered monochromatic light, as your question indicates, the coherence length could be infinity. The same is true for the radio band systems formula for the coherent length, $\Delta f$ is in the denominator over there, too.
• That's a good point. One could perhaps isolate discrete spectral lines and estimate their real-world $\Delta \lambda$. But much of the solar radiation is a continuous black-body radiation - radiation at all frequencies in the interval - so there's no natural way to separate it to discrete lines with some width. Jun 29 '14 at 13:52