Shadows Art

Length of Shadow = Tan(θ).a : Where a = object's height, and θ = angle between the point of light and the object. Shadow length 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.
For a non-point source of light, the shadow is divided into the umbra and penumbra. The wider the light source, the more blurred the shadow. If there are multiple light sources there are multiple shadows, with overlapping parts darker, or a combination of colors. For a person or object touching the surface, like a person standing on the ground, or a pole in the ground, these converge at the point of touch.