What happen to the length of the shadow from sun rise to sunset in one day?

Answer 1

The length of an object's shadow is equal to the height of the object divided by the tangent of the angle of the sun's elevation above the horizon. At sunrise, when the sun's elevation is 0, the length of shadows is (theoretically) infinity. Shadows get shorter as the sun's elevation increases. Since the tangent of 45° is 1, when the sun's elevation is 45°, half way between the horizon and straight up, the length of the shadow of an object is the same as the height of the object. At apparent solar noon the sun's elevation is at its maximum for the day, so the length of an object's shadow is at its minimum for the day. On the equinoxes that length is approximately the height of the object times the tangent of your latitude. Also, at apparent solar noon on the equinoxes, all shadows in the northern hemisphere point due north, and all shadows in the Southern Hemisphere point due south. Between the tropics and the polar regions, that is true of every day. If the sun were directly overhead, which cannot happen north of the Tropic of Cancer or south of the Tropic of Capricorn, the sun's elevation would be 90°. The tangent of 90° is infinity, so the length of a shadow is 0. Finally, as the sun's elevation decreases from apparent solar noon until sunset, shadow lengths increase.

Answer 2

The length of a shadow is longest at sunrise and sunset when the sun is lowest in the sky. As the sun rises higher in the sky, the shadow becomes shorter. At solar noon, when the sun is directly overhead, the shadow is at its shortest or disappears completely.