Shadow Length Lab
Move the sun across the sky and watch how shadows change. Set your object height, choose a time of day, and record measurements to discover the trigonometric relationship between sun angle and shadow length.
Guided Experiment: Shadow Length Investigation
At what time of day do you predict the shadow will be shortest? What do you think will happen to shadow length as the sun gets higher in the sky?
Write your hypothesis in the Lab Report panel, then click Next.
Setup
Adds the current time, sun angle, and shadow length to the data table.
Controls
Data Table
(0 rows)| # | Time | Sun Angle(deg) | Object Height(m) | Shadow Length(m) |
|---|
Time of Day vs Shadow Length
Reference Guide
How Shadows Form
A shadow forms when an object blocks sunlight. The sun travels across the sky in an arc from east to west. The angle between the sun and the horizon is called the elevation angle.
When the sun is low on the horizon (small elevation angle), its rays hit objects at a shallow angle and cast long shadows. When the sun is high in the sky (large elevation angle near noon), rays hit more steeply and shadows are short.
The Trigonometry Formula
The shadow length depends on object height and the sun's elevation angle:
where theta is the sun's elevation angle. At 45 degrees, shadow length equals object height (tan 45 = 1). At lower angles, shadows get much longer.
Sun Angle and Seasons
The sun's maximum elevation at noon depends on your latitude and the time of year. At 40 degrees N latitude in midsummer, the noon sun reaches about 70 degrees. In midwinter, it stays below 30 degrees.
This lab uses approximate elevations for a mid-latitude summer day. At the equinoxes (spring and autumn), noon elevation is roughly 90 minus your latitude.
Sundials Through History
Ancient Egyptians and Babylonians used shadow lengths to tell time. A gnomon (the upright pointer on a sundial) casts a shadow whose length and direction reveal the time of day.
Surveyors and navigators once used shadow measurements to determine latitude. If you know the sun's angle at noon on a specific date, measuring the shadow of a known-height object gives your latitude.