Color of the setting Sun

Nice Earth Science Picture of the Day for yesterday - Sunday, May 15 (visit the site for a larger image and explanation).

Why does the Sun look yellow in the sky?  Why is the setting Sun red?  Why is the sky blue?  All related questions that most people understand as having to do with the scattering of different wavelengths of light in our atmosphere (although many of my students can't explain it well when asked to do so on an exam).

There are a couple of things going on with regards to this phenomenon.  Let's start with the figure at right.  It shows how you have to look through a thicker layer of the atmosphere when you look at the Sun near the horizon than you do when it's higher in the sky.

Second, understand that light from the Sun is white light, a mixture of all different wavelengths (colors).  As light from the Sun passes through the atmosphere, the shorter wavelengths of light (the blue end of the spectrum) are scattered more than the longer wavelengths of light (the red end of the spectrum).

Why are different wavelengths of light scattered differently?  The blue sky is caused by Rayleigh scattering - named after the English physicist John William Strutt, aka Lord Rayleigh (1842-1919).

Rayleigh worked out an equation explaining how much different wavelengths are scattered by molecules of oxygen and nitrogen in the atmosphere.   It's basically due to the electromagnetic energy waves interacting with the electrical charges of small atoms and molecules.  I won't go into the derivation of this since it's very messy and I don't fully understand it myself but here's one version of the equation:

Forget about most of the terms (for a nitrogen molecule in the Earth's atmosphere, for example, we can assume all of the variables are essentially fixed to some value), the important term is lambda (l) raised to the fourth power in the denominator.  This denotes the wavelenth of the light that will be scattered.

Red light at, for example, a wavelength of 625 nm will give a larger value in the denominator when raised to the 4^th power than will blue light at a wavelength of around 450 nm.  A larger value in the denominator of a fraction will result in a smaller value for the overall fraction.  In other words, blue light, at a wavelenth of 450 nm, will be scattered 3.7 times more than red light, at a wavelength 625 nm.

This is why the sky is blue.  As white light comes in from the Sun, the shorter wavelengths of blue light are scattered around in the sky by nitrogen (N₂ = 78% of our atmosphere) and oxygen (O₂ = 21% of our atmosphere) molecules making it all appear blue in color.

Why are clouds white?  Because the water droplets that make up clouds are much larger than the nitrogen or oxygen molecules in the atmosphere.  Rayleigh scattering only works when the particles are less than about 1/10 of the the wavelength of radiation of the electromagnetic energy.  For water droplets, a different type of scattering occurs for light which is not wavelength dependent.  Water droplets scatter all wavelengths equally making clouds look white.

By the way, for longer wavelength microwaves, water droplets will actually cause Rayleigh scattering and this is how weather radar works.

Back to the setting Sun which started this discussion.  From orbit, the Sun is blindingly white.

From the Earth's surface, however, we perceive it has color.  When it's high in the sky, and we see it through a thinner layer of atmosphere, only the bluest wavelengths are scattered out and our eyes average the rest of the wavelengths into a yellow color.  When it's setting, however, we're looking at it through a thicker layer of the atmosphere, and most of the wavelengths are scattered away and only wavelengths from the red end of the spectrum reaches our eyes.  Therefore, a reddish setting Sun.

Isn't science wonderful?

Addendum:  Today's Earth Science Picture of the Day shows the same effect for the Moon.