Shadows

A shadow is an area where direct light from a certain light source cannot reach due to obstruction by an object. It occupies all of the space behind an object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or reverse projection of the object blocking the light.

Length of Shadow = Tan(θ)*a. Where a = object's height, and θ = angle between the point of light and the object.

Shadow length will change quite 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.