Why the sky is blue.

Why is the sky usually blue? Why is it red at sunset and sunrise? Rayleigh scattering.

This is something we discussed in our Electrodynamics course. Explaining the maths behind it would be tedious. I’m just going to through you a result and then we’ll talk about the physical implications.

Rayleigh scattering.

It is the process in which a photon (light) collides with a (small enough) particle and its direction is altered:

Each light wave has a different wavelength.

It turns out the smaller the wavelength, the more likely is scattering to happen. 

This has intuition. The smaller the wavelength, the higher the frequency of oscillations:

A bit more precisely, the Rayleigh cross-section () is defined to be the scattered power divided by the incident power. The bigger , the more often scattering takes place. We have .  So the scattering rate depends inversely proportional* on the fourth power of the wavelength, .

*(At least in an approximation regime: dipole limit, non-relativistic oscillations, far-field approximation)

The colour of the sky

So, how can we use this to explain the sky’s colour?

The colours we see, the visible spectrum, are just light waves with different wavelengths:

Blue has a shorter wavelength than red.

So blue light scatters more than red light.

• When the Sun is high in the sky, if you look around you see mainly blue light. It is scattering around the atmosphere. Some of it is directly scattered back to you. If you look directly at the sun, it’s white (all of the colours) since some of the rays have not been scattered yet.

  

• When the Sun is on the horizon (sunset or sunrise), you see the red light that has not been scattered. Blue and other colours have been scattered to the Earth or the atmosphere long before the lightray reached you. You see the Sun red.

Nice, isn’t it??

Well, that’s a good point to end if you have had enough.

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However, it turns out that the whole thing is more complicated. Why?

Of course, surely there must be quantum and relativistic corrections for Rayleigh scattering (but presumably negligible for this case). But that is not my the point of my question.

There is a small gap in the logical argument above. It all seems sensible. It all seemed sensible to me when I first come across this. But after I wrote the above part of the post, I got hit with a question:

WHY IS THE SKY NOT PURPLE?

Following the above logic: Purple is the (visible) colour with the smallest wavelength. So it is the colour that is scattered most to the atmosphere (even more than blue).  Hence, during day time, we should see the sky purple and not blue!

Well, the sky is not purple because of a combination of other factors. You can read about them here: Why is the sky not purple? (Physics Stack Exchange)

While doing some searches for this post, I came across this page of NASA.  It shows essentially the same idea I used to explain why the sky is blue. At the end, there is  another related very good question:

IS THE SKY BLUE IN OTHER PLANETS, TOO?  No! It’s reddish in Mars, for example…(Check out the link for more.)

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Okay, that’s enough (for now, at least).

Acknowledgements: Thanks to Prof. Dorey for the lectures on electrodynamics!    Disclaimer: I’m a student – I might have gone wrong somewhere. Comments/errors spotted are very welcomed!

Thanks for reading! Until the next one.

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PS: After I finished writing the post, I looked through my window. This was Madrid’s sky at around 6pm that day: