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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“Little minds mistake little objects for great ones, and lavish away upon the former that time and attention which only the latter deserve. To such mistakes we owe the numerous and frivolous tribe of insect-mongers, shell-mongers, and pursuers and driers of butterflies, etc. The strong mind distinguishes, not only between the useful and the useless, but likewise between the useful and the curious.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)