Why do shadows stretch out and try to merge?

Answer 1

there is a simple effect and a complex effect at work here. The simple effect is due to the fact that the sun is not a point source, meaning the sun appears as a disk of light instead of an infinitesmally small point of light. The sun subtends about 1/2 of a degree in the sky instead of zero degrees for a perfect point source. If you trace the rays from the sun you will find that along the edges of an obstruction (your hand, for instance), not all of the suns rays are blocked. The result is a 1/2 degree blur in the edges of shadows. The extent of the blur is 2*d*tan(.5) where d is the distance from your hand to the wall. If your hand is four feet from the wall, the blur would be about 0.84 inches, or a little more than three quarters of an inch. The blur gets larger as your hand moves away from the wall, so the shadow cast by your hand appears to merge with the shadow of your head.