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I have been trying for a couple of days to come up with a nice illustration of why crepuscular rays are not suggesting that the sun must be close to the earth, as flat-earthers claim.

enter image description here

I made the following 3D-diagram to show how parallel rays (pointing to a source at an infinite distance), and converging rays (pointing to a close source $P$) are in fact indistinguishable to an observer, since they produce identical projections on a canvas:

enter image description here

This was made using GeoGebra. One can play with it, move around $P$ and rotate the view by following this link to the diagram on GeoGebra-tube.

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My goal is to make the illustration as powerful and simple as possible, so I am asking for suggestions to improve it.

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    $\begingroup$ Asking for "suggestions to improve" an illustration is not a physics question, and doesn't have an objectively correct answer. $\endgroup$
    – ACuriousMind ♦
    Commented Jun 20, 2016 at 13:44
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    $\begingroup$ Debating a flat-earther, hunh? If your goal is to find out which of you is the cleverest, or which of you knows more about the construction of valid vs. fallacious arguments, then go for it. Have fun! If, on the other hand, your goal is convince the flat-earther that the Earth is not flat, then you might want to stop and think about why somebody would say such things when they live in a world where airplanes and satellites circle the globe every day $\endgroup$
    – Solomon Slow
    Commented Jun 20, 2016 at 14:16
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    $\begingroup$ Many examples by Les Crowley, and many more buried in his daily archives. You might consider simultaneously discussion crepuscular and anti-crepuscular rays. $\endgroup$
    – rob ♦
    Commented Jun 20, 2016 at 15:46
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    $\begingroup$ The only correct reaction to meeting someone like that is to turn around and walk away slowly, hoping that the madman will not attack you from behind. :-) $\endgroup$
    – CuriousOne
    Commented Jun 20, 2016 at 22:50
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    $\begingroup$ Maybe try animating that to show how this L2 slowly goes to L1 still giving the same projection on the screen? These people are not used to read diagrams. I think animation wold be the most instructive for them. $\endgroup$
    – Licho
    Commented Jun 21, 2016 at 4:49

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To get a full account of this buy the Dover edition of the book by van de Hulst "Light Scattering by Small Particles." This involves Mie scattering, which is more general than Rayleigh scattering at the red or IR regime. The scattering has intensity lobes, similar to antenna lobes in electromagnetic applications, and what these crepuscular rays are the appearance of the maximum Mie scattering intensities at different regions in the atmosphere. Consequently what you are seeing are not rays moving through the clouds, but rays that are scattered by small particles or dust below the clouds. The divergence of these rays it not because of the direction light is traveling from the sun. but the visual occurrence of the maximum on the scattering lobe.

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  • $\begingroup$ Interesting! So the different sources explaining it as merely an illusion due to perspective are not in fact correct? Does that mean that my model is entirely misleading? Or does it have some value after all? $\endgroup$
    – String
    Commented Jun 20, 2016 at 17:35
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It's just a case of a perspective. I've just modeled it in blender to see how it should look like making sure that the beams are perpendicular. That's what i get.My model is not perfect but you see what's going on. enter image description here

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A suggestion would be to include straight standing lines that represent buildings. And also include the angle of the rays of the sun with respect to the horizontal ground at a specific time. And compare using the known angle from the ground, whether it is really the converging rays, or parallel rays that will produce such projections: enter image description here


The angle can be easily known by planting a straight stick near the viewpoint such that is won't produce any shadow, then measure it with a protractor.
But then again, the flat-earther might notice that "of course the angle of light at the location we view it is actually different and more smaller than the angle at the location where L2 hit the ground if the rays were convergent, so this does not prove anything":) enter image description here
The task will then be to prove that the angle we see at the viewpoint is quite the same as the true light angle where L2 or L1 hit the ground and other relevant areas (maybe measure those points too, if we can?).
To do this, one might construct a solar-angle table, which relates the angle of the sun with respect to the clock time. Then one could argue that the clock time at the location where L2 or L1 hits the ground and the clock time at the viewpoint is quite the same, (since the light hits the ground of the same country) therefore, it should have quite the same angle, and therefore, it is indeed the perspective view of parallel rays that is causing the said projections on the canvas.

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