Why do shadows stretch and shrink?
Turn on a lamp and a shadow appears behind you. A shadow is not an object; it is a patch of ground that receives no direct light. Light travels in straight lines, your body blocks some of those paths, and the blocked region becomes the shadow—always on the far side of the lamp.
To predict how long a shadow is, follow one line only: the boundary ray that grazes the top of your head. It leaves the lamp, skims the head, and lands on the ground at the shadow’s tip.
- Lower the lamp and the boundary ray becomes shallower, travelling farther before it lands. The shadow grows. Brightness has nothing to do with length; only position matters.
- Raise the lamp and the ray steepens, landing sooner. The shadow shrinks.
- Use a taller object and a higher path gets blocked, so the boundary lands farther away.
The Sun works the same way. A low morning Sun casts long shadows; a high noon Sun shortens them; when the Sun sinks on the other side, the long shadow switches direction. What changes is the angle of the light, not the Sun’s strength.
Three flashlight experiments
At night, find a wall or floor, a flashlight and a small toy. Change only one thing at a time:
- Height only. Raise and lower the flashlight while keeping its brightness fixed. Watch the shadow’s tip travel away and return.
- Object only. Swap in a taller toy with the lamp fixed. See where the boundary ray lands.
- A whole day. Sweep the flashlight along a wide arc: low on the left, overhead, low on the right. That is one “day” of shadows on the ground.
Guess first: if the lamp moves to your other side, what happens to the shadow? Then test it. Direction words can mislead; objects cannot—keep your eye on the tip.
Point sources, parallel rays and soft edges
Open: the geometry of two light sources
A nearby lamp can be treated as a point source. With lamp height H_L, head height h and horizontal distance d, similar triangles give the shadow length:
The Sun is so far away that its arriving rays are essentially parallel. With the Sun’s elevation α:
At α = 30°, the shadow is about 1.73h; at α = 60°, about 0.58h. Both ratios can be checked in the experiment above.
Open: why are shadow edges soft?
A real bulb and shade have size; they are not infinitely small points. Different points on the source draw slightly different boundary rays that land at slightly different spots. The region that receives no light at all is the umbra; the region receiving partial light is the penumbra—the soft edge. A larger, closer source makes the soft edge wider.
Limits of the model
This explanation uses flat ground, straight-line propagation and simple source shapes. Complex silhouettes, uneven terrain, scattering by clouds and small-scale diffraction are out of scope. When the Sun is very low, the shadow becomes longer than any picture can hold; the scene marks it “extending beyond the frame” instead of shrinking the person to fake a fit.