# Penetration of light in the atmosphere

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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