BUT...in your example, the person's hands are BIGGER than the light bulb!
put a lamp in the middle of the room, and you could make big shadow puppets on one wall but have NO shadows on the opposite wall.
so you think the sun is like a spotlight, in that it sends it's light ONLY in ONE direction?
then explain how VENUS is sometimes visible during the day!
if the object was smaller than the sun, it would only block PART of the sun, making a black spot on the sun but only making a small reduction in brightness!