Determining the Length of a Shadow

The location of the light source and the height of the item generating the shadow are the two main parameters that determine how long a shadow is. This is a calculation formula along with an explanation of how these elements affect shadow length.

Position of the Light Source

An object’s shadow length is determined by the angle at which light strikes it. Longer shadows are produced by objects when a light source is low on the horizon, such as the sun at dawn or sunset. This is because the shadow becomes longer when light strikes an item at an oblique angle. On the other hand, things cast shorter shadows or none at all when the light source is directly above, such as the sun at midday.

Height of the Object

An object’s height is a major factor in determining how long its shadow is. Generally speaking, when an item is lit from above at a certain angle, the longer the shadow it produces, the taller the thing is. This is because a larger patch of darkness, or shadow, is created when an item blocks more light.

To find the length of a shadow, you need to know the angle of the light source and the distance from the object to where the shadowlands. Measure how far the object is from the spot where its shadow touches the ground. Then, multiply this distance by the tangent of the light source’s angle. If the angle is less than 10 degrees, you can use this simple formula: Length of Shadow = Distance to Shadow Point × tan(Angle of Light). For greater accuracy or larger angles, you might need more complex math.