Why is 8 am (just after sunrise) darker than 12 pm (noon)? Does it have something to do with the geometry of spheres? Or is it due to the atmosphere?
Answer
The main factor is geometry. The Sun doesn't change, and it emits a constant "radiant intensity", defined as "luminous flux per solid angle"
$I=\frac{dF}{d\Omega}$
And the illumination depends on it. Imagine a disc on the ground. Of course it is much more illuminated if the source is opposite to it. Explicitly, the illumination is
$ \frac{dF}{dS_2}=\frac{Id\Omega}{dS_2}=\frac{I\cdot \cos\alpha_2}{r^2}$
And so the illumination directly depends on the cosine of the angle of incidence. That's why you want to sunbath perpendicularly.
Besides this, the atmospehre plays also a role. When the rays are not perpendicular, they must travel along more thickness, so they are very slightly mittigated (thats why you shouldn't sunbath too much at noon). But this effect is much more noticeable as for the scattering of wavelenghts. That's why sunset and sunrises look red. Check this image:
https://thesciencegeek01.files.wordpress.com/2015/09/redsunsetdiagram1.png
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