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Chad over at Uncertain Principles had a nice “Basic Concepts” article on estimation and dimension, things like order of magnitude calculations and dimensional analysis. Nice, right until the end. Here’s what I dislike:
A nice example of this comes from my recent bedtime reading, Götz Hoeppe’s Why the Sky Is Blue, which describes how Lord Rayleigh determined the wavelength dependence of the scattering process that bears his name using nothing but dimensional analysis. He recognized that there are only a handful of things that can possibly affect the intensity of the light scattered from particles in the air: the wavelength of the light, the size of the particles, the density of the particles, the density of the surrounding medium, and the distance between the scattering particles and the observer. Using simple dimensional considerations, he was able to deduce that the scattering intensity has to be inversely proportional to the fourth power of the wavelength, which is the correct dependence. And, incidentally, explains why the sky is blue.
Rayleigh scattering does indeed depend on the inverse fourth power of wavelength, but given that our vision sensitivity doesn’t stop at blue, but extends into purple, Rayleigh scattering should mean the intensity of scattered light which has a maximum is in the purple, not blue. So why is the sky blue instead of purple?
The answer should be obvious, but most physicists that mention why the sky is blue fail to follow through and give the full explanation: the physiology of the human eye. The Wikipedia page on colour vision has this nice plot showing the response of the eye to various colour stimulation:
Our eye absorbs light better in the blue (with a maximum around 420 nm, but the specific value varies from person to person) than in the purple. The sky is blue not just because of Rayleigh scattering, but also because our eyes are more sensitive to blue light on that end of the spectrum.
Biocurious is written by Andre Brown and Philip Johnson, since 2005. Content of the weblog is licensed under a Creative Commons Attribution-Share Alike 3.0 License.
The book I got the Rayleigh derivation from talks at length about the numerous phenomena that go into making the sky blue, and there’s more than one thing there. After all, if you just kept applying the Rayleigh scattering formula, you’d expect a peak in the ultraviolet, X-ray, or gamma region of the spectrum, not purple.
I don’t have the book here with me, but it claims that there is a real, physical peak in the spectrum of light scattered from the sky somewhere in the high 400’s. Wikipedia provides an image with a peak just shy of 500 nm, but there are some non-ideal conditions detailed in the caption, so I’m not sure how much I’d trust it.
I’ll take another look tonight, and see what they give for the peak wavelength, but I’m pretty sure that the peak is higher in wavelength than what I would usually call purple.
I always wanted a professor to ask me the blue sky question on a qualifying exam. Then I could give them the Rayleigh explanation and ask them why the sky isn’t purple :)
I think that the sky should be purple because it does have a lower frequency than blue light. Why do human eyes have to be like this?
Thanks for the explanation. Anyway, thanks to god for making our eyes more sensitive to blue than to purple because although a purple sky is very beautiful, I’d prefer blue one!
http://www.georgeaugustkoch.com/ImageFolder/PurpleSky.jpg