Suppose that a high-voltage electrical power cable, 2 cm in diameter, is 15 mete

Question

Suppose that a high-voltage electrical power cable, 2 cm in diameter, is 15 meters above the ground, which happens to be flat. (Yes, I know that power cables hang, so that different bits of it are different heights above the ground, but ignore that complication.) Let's further assume, for the sake of simplicity, that the sun is directly overhead. The cable casts a shadow on the ground. Is any part of that shadow in the umbra, or is it entirely in the penumbra? How wide is the shadow? Is the shadow of uniform darkness on the ground? If not, can you describe how its darkness varies with position?

If there was another power cable at the same height that was 3 cm in diameter, how would its shadow compare to the shadow of the 2 cm cable? Would it be 1.5 times wider? (Or more or less than that wide?) Would it be the same darkness?

Explanation / Answer

The shadow is in penumbra. maximum wide is 2cm. The shadow is not uniform darkness. The darkness decreases from the centre.

in case of 3cm wide cable, the thickness of shadow is proportionately wider.

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