# Rayleigh Scattering, Atmosphere-Dependant

I've come across the Wikipedia article on Rayleigh Scattering and it quotes that

In detail, the intensity $$I$$ of light scattered by any one of the small spheres of diameter $$d$$ and refractive index $$n$$ from a beam of unpolarized light of wavelength $$λ$$ and intensity $$I_0$$ is given by

$$I = I_o \left(\frac{1 + cos^2\theta}{2R^2}\right)\left(\frac{2\pi}{\lambda}\right)^4\left(\frac{n^2-1}{n^2+2}\right)^2\left(\frac{d}{2}\right)^6$$

In another article, it says that a hydrogen-dominated atmosphere exhibits stronger Rayleigh scattering effect as compared to an atmosphere which is oxygen-dominated. From the formula quoted above, I can't see how is this so. In any way, the "particle size" of a hydrogen molecule is probably less than that of an oxygen molecule. If $$d$$ was the factor, it would have said that the intensity of the scattered light should have been lower, contradicting the statement above.

Is there another way to think about this problem and possibly explaining the difference in the scattering effect in two different atmospheres?

• Welcome to Physics SE! Can you include in your question a link to the source of your second statement? For example, if it refers to Rayleigh scattering by exoplanet atmospheres the extent of the atmosphere is the essential factor. – user197851 Dec 8 '18 at 9:39
• The source can be found here: (exoplanets.nasa.gov/resources/168/…) Yes I do agree that the extent plays a role. For instance, in the source, it is clear that if we compare two different extents of the atmosphere, the scattering effect does differ. However, I didn't quite catch on how a water-rich atmosphere has a scattering effect that is weaker than a hydrogen-dominated one, as implied by the source. Thanks in advance! – HK Tan Dec 8 '18 at 11:36

## 1 Answer

In line with the general guidance (not to put answers in comments), I'll offer this bare-bones answer. However, I'm sure that real experts can give much more comprehensive ones: I am not an expert on planetary atmospheres! You may wish to wait for those answers.

It looks like the source of the claim

a hydrogen-dominated atmosphere exhibits stronger Rayleigh scattering effect as compared to an atmosphere which is oxygen-dominated

was this web page on exoplanet atmospheres. So "stronger Rayleigh scattering effect" needs to be set in that context. Integrating the given formula over angles gives the scattering cross section per particle. Then the total amount of scattering (as a function of wavelength) will involve integrating along the path of the light (in fact, over all the parallel paths which pass through the atmosphere at various heights): the extent of the atmosphere as well as the density of molecules in the atmosphere will enter the formula. What is left (the spectrum of unscattered light) is what we observe.

So the bottom line is that the quantities in that equation are not the only ones affecting the overall Rayleigh scattering of light passing through planetary atmospheres. As I said, I am sure that more detail can be given.