Tuesday, January 13 2009
Why Is the Sky Blue?
Blue skies
Smiling at me
Nothing but blue skies
Do I see
Irving Berlin was a lyricist, not a physicist, but he knew a good thing when he saw it. Blue skies turn out to have a precise connection to the colour of wine. No, not blue wine--that's for Romulans and cosplay geeks, but rather why wine made from my kits is darker after it's been filtered, and why the sky is blue and not some other colour.
It turns out all of this can be laid on the feet of a chap named John Strutt, also known as Lord Rayleigh.
Look! It's Donald Sutherland!
Rayleigh was one of those gigantic Victorian brainiacs who tower over early science. Cavendish Professor of Physics, Royal, Copley and Rumford medals, Nobel prize, etc. I bet he thought he was so smart, grumble.
Ahem, my intellectual inferiority complex aside, Rayleigh answered the question that every kid asks when they're trying to squeeze a few more moments of consciousness out before bedtime, 'Why is the sky blue?' Air is clear, the particles floating in it are too small to show colour, and the sky doesn't reflect water (as an uncle told me once). If that were all there were to it, the sky should be jet black, like it is on the moon.
And they said the moon landings were fake!
Of course, that's not all: Rayleigh Scattering is a process in which electromagnetic radiation (including light) is scattered by a small spherical volume of variant refractive index, such as a particle, bubble, droplet, or even a density fluctuation. The sky appears blue because the wavelength of blue light is shorter than that of other observable colours so it gets scatterd more. How much more?
Warning! Math ahead.
Rayleigh's model says that the scattering of the light by molecules in the atmosphere goes according to the 4th power of the wavelength. Blue light runs 450 nanometers (when I was a kid it was 4500 angstroms, but I guess inflation catches up with everything). Red light runs at 600 nm. To get mathy, blue light is (600/450)4 times more likely to get scattered than red. Therefore
600/450 = 1.33 . . .
1.33 x 1.33 x 1.33 x 1.33 = 3.2
So blue light gets scattered and diffused 3.2 times more than red.
All wavelengths of light scatter, it's just that blue is hit worst. If you look straight up, you're gazing through the thinnest layer of atmosphere and you'll see the bluest sky because that's where the fewest other wavelengths get scattered. Look off towards the horizon (and thus through a really thick layer of atmosphere) and the light can even look white–and brighter–because so much more light is scattered over the long journey though all that air. This also explains why icebergs are blue! Cue the Discovery Channel Song!
So, I hear you ask, where does that leave wine, Mr. Wizard? Glad you asked. If things appear white because they scatter the light hitting them, finished wine with a whole lotta goo floating in it scatters like crazy. This takes the colour from deep and clear and lightens it to muddy and light as the wavelengths hit floaty yeast cells and other suspended material.
Same stuff, just not on the same wavelengths
This leads us to the odd and counter-intuitive derivation: filtered wine is darker than unflitered. Seems wacky, but if you can't beleive it, I blame Lord Rayleigh.
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