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Why do sunbeams diverge even though the sun is much more than a few kilometers away?

user56903 · 2014
Stack Exchange · Datasets · License: CC BY-SA · 2014
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everyday-lifegeometryphysics
Consider this picture of sun beams streaming onto the valley through the clouds. Given that the valley is only (at a guess) 3km wide, with simple trigonometry and the angles of the beams, this gives the result that the position of the light source is being a few tens of km away at most. What is wrong with the analysis?
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