A shadow is a dark region that appears when an opaque object blocks the path of a light source. Since light travels in straight lines, the shape and size of this dark area depend on the relative positions of the light source, the object, and the surface it falls upon. The daily variation in shadow length, caused by the Earth’s rotation changing the Sun’s position, is a universal experience.
The Time of Maximum Shadow Length
Shadows reach their maximum length twice daily: immediately following sunrise and just before sunset. At these times, the Sun is situated at its lowest point in the sky, appearing to skim the horizon. This low-angle position causes the light rays to strike the ground at the shallowest possible angle. The result is a long shadow that stretches far away from the object casting it. The moment the Sun’s disk is halfway visible above the horizon marks the beginning and end of the shadow-casting potential for the day.
The Science of Solar Altitude
The geometric relationship between the Sun and a cast shadow is governed by solar altitude, which is the angular height of the Sun above the horizon. When the solar altitude is low, the light rays travel through a greater amount of the atmosphere. This shallow angle of incidence causes the light rays to spread out across a much larger area of the ground surface.
The mathematical relationship dictates that a lower angle creates a longer shadow relative to the object’s height. For instance, when the Sun is at a 45-degree angle above the horizon, the shadow length is exactly equal to the object’s height. As the angle decreases toward the horizon, the shadow length increases because the light source is nearly horizontal to the ground.
When Shadows Are at Their Minimum
The shortest shadow of the day occurs at solar noon, which is when the Sun reaches its highest point in the sky. Solar noon is defined by the Sun crossing the local meridian. It rarely aligns perfectly with 12:00 PM on a clock due to time zones and the Earth’s orbital variations.
At this peak altitude, the light rays strike the Earth in the most vertical, direct manner. This steep angle concentrates the light, minimizing the shadow’s spread on the ground. For locations within the tropics, the Sun can be directly overhead at a 90-degree angle twice a year, resulting in a “zero-shadow day.” For all other locations, the shadow reaches its smallest possible size for that specific day.
The Influence of Season and Location
While the daily cycle dictates the transition from long to short to long shadows, the overall possible length is influenced by season and geographical location. The Earth’s tilt affects the maximum solar altitude the Sun achieves at solar noon, meaning the shortest shadow of the day changes length throughout the year.
During the winter solstice, the Sun reaches its lowest maximum altitude, resulting in the longest noon-time shadow of the year. Conversely, the summer solstice brings the highest maximum solar altitude, producing the shortest noon-time shadow. Locations closer to the equator experience higher solar altitudes year-round, leading to smaller overall shadow variations compared to higher latitudes.