Variation With Time
Shadow length when caused by the sun changes dramatically throughout the day. The length of a shadow cast on the ground is proportional to the cotangent of the sun's elevation angle—its angle θ relative to the horizon. Near sunrise and sunset, when θ = 0° and cot(θ) is infinite, shadows can be extremely long. If the sun passes directly overhead, then θ = 90°, cot(θ)=0, and shadows are cast directly underneath objects.
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“The prince in disguise makes the most charming beggar in the world, no doubt; but that is because—as all fairy-tales from the beginning of time have taught us—the prince wears his rags as if they were purple. And, to do that, he not only must once have worn purple, but must never forget the purple that he has worn. And to the argument that all cannot wear purple, I can ... only reply that that seems to me to be no reason why all should wear rags.”
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