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The sky looks blue because of scattered photons. Our Sun looks often yellow because the photons we receive in ours eyes 'are' yellow. Now is the yellow light we receive in our eyes when looking straight into the sun (I know it is not recommendable) coming straight from the sun? If so what percentage of sun rays goes straight into our eyes and what percentage is scattered?

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  • $\begingroup$ About 75% (clear sky!) of the TOA flux reaches the surface. $\endgroup$
    – user107153
    Commented Aug 3, 2017 at 19:53

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The extinction in the atmosphere varies with the amount of dust and aerosols and of course at what elevation you are looking at.

A typical value at a good astronomical site at about 550nm would be around 0.1 mag per airmass. In "real" units, this means that 90% of light at the top of the atmosphere (of a star or indeed the Sun) makes makes it straight through the atmosphere if the star/Sun was directly overhead. The amount of scattering would then increase with angle from the zenith $z$ as $\sec z$ (an approximate formula that works reasonably for say $\sec z < 5$. It would also increase dramatically at bluer wavelengths (roughly as $\lambda^{-4}$) where the scattering becomes dominated by Rayleigh scattering from air molecules.

At sea level and at more "normal" places on Earth, you could scale up the scattering by factors of 2-3 or even more. But this is usually because of dust and pollutants rather than scattering from air molecules.

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Here's a handy chart from Wikipedia showing the difference between the amount of solar energy hitting the top of the atmosphere (yellow) vs. the amount that makes it to sea level (red):

enter image description here

To estimate the total energy (per area) over a range of wavelengths, look at the area under the curve between these two wavelength. Eyeballing this graph, I would say that approximately 1/3 of the visible light energy is lost, about 3/4 of the UV light energy, and no more than about 1/4 of the infrared light energy.

I should note some technical details: The amount of solar energy that makes it to the earth's surface depends on a lot of factors, particularly the density of air molecules in the atmosphere (which is affected by atmospheric pressure & temperature), the amount of water vapor present, the amount of ozone present, aerosol pollutants, etc. The red spectrum above represents an average over the course of a year at a typical latitude in the continental USA. As far as I can tell, it does not account for cloud cover when taking this average; in other words, this would be an average for a clear day with a typical amount of water vapor, ozone, and aerosols in the atmosphere above you. You can read about the nitty-gritty details here if you're interested.

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  • $\begingroup$ Thanks, but I'm not sure if this answers the question, because in my question both the straight and the scattered photons are all going through the atmoshpere $\endgroup$
    – Marijn
    Commented Aug 3, 2017 at 18:55

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