Rayleigh Scattering: Blue/Red Irradiance Ratio & Distance

[e101101]

Homework Statement

General question

Relevant Equations

I is prop to λ**(-4)

Hi everyone, does the scattering irradiance ratio between blue/red change with distance with Rayleigh scattering?
I would think that it would remain generally constant..

 

[Charles Link]

A little info that should provide some helpful hints: When the sun is overhead, the light has about 10-20 miles of atmosphere to go through to reach you. The blue light gets scattered out more than the red light, but for both colors through this relatively short distance, greater than 90% of the light reaches the observer. When the sun is on the horizon, the light from the sun goes through perhaps 100 miles or more of atmosphere to reach the observer, because the atmosphere is a thin ring of about 20 miles thickness, on the circular (spherical earth) with a radius of about 4000 miles. $\\$ That should explain why the sun appears red or orange in a sunset, but looks white when viewed overhead. If you do a little arithmetic logic with this info, it should provide the answer to your question.$\\$ (Note: blue light has a wavelength approximately half that of red light).