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While I was considering an answer to this question, I wondered how much light that enters the atmosphere reaches the ground without colliding with air molecules—if any. I've taken a good bit of physics course (not optics, yet), but I'm not really sure how light interacts with gases or other transparent material. I've always thought that it's periodically absorbed and then reemitted at a similar or identical angle and energy. I know I'll learn about it at some point, and I'll probably read up on it sooner than that, but to make it more fun, I'll ask these questions first:

What fraction of the light that enters the earth's atmosphere reaches the ground "unmolested"—without ever colliding with an air molecule? Is there practically any?

If no light can traverse the atmosphere without interacting with air, then what fraction of it reaches the ground without significant changes to its direction and/or energy? I imagine that this has a frequency dependency (i.e. the sky is blue, UV filtering).

Well, there you have it. Now I'm going to try to focus on my real homework.

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The light you see as the image of the Sun on the sky is basically undeflected.
http://en.wikipedia.org/wiki/Diffuse_sky_radiation says it is 75 % when the Sun is high and the sky is clear. The frequency dependency is due to Rayleigh scattering.
For the cloudy sky the fraction is much smaller, up to many orders smaller than unity (maybe 1 millionth part as a wild guess).

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Regarding your question about changing direction:

If no light can traverse the atmosphere without interacting with air, then what fraction of it reaches the ground without significant changes to its direction

Remember that air has an index of refraction different than the vacuum of space (about 1.00027 for air versus 1 for space). The index of refraction represent the electromagnetic waves of light interacting with the electric field of the air molecules to be deflected.

In this sense, absolutely no light passes through the air "unmolested".

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  • $\begingroup$ So it's refracted but not scattered? I always had wondered what the index of refraction was from. It makes sense, though. Thanks! $\endgroup$ – krs013 May 17 '13 at 22:44
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    $\begingroup$ @krs013 some of the light is scattered. All of it is refracted. The refraction happens because the electric field changes the speed the light propagates and that changes the angle. Even light completely normal to the atmosphere (90 degree angle) is refracted because the atmosphere isn't a perfectly uniform temperature and density and it causes the light to be refracted somewhat randomly. This is what "adaptive optics" in ground telescopes corrects for. $\endgroup$ – Brandon Enright May 17 '13 at 22:47

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