Why does a tree’s shadow move and change length?

Move the Sun and watch the shadow of a marked point 5 metres above level ground.

Before you try

If the Sun is lower in the sky, does this shadow become longer, shorter, or stay the same?

01 / Height above the horizon

A light ray meets level ground

Reference shadow seen from the sideA five-metre pole beside a tree casts a shadow. Marked top · 5 m 10 m
5.00 mreference shadow length

Fixed scale. The measured shadow belongs to the marked pole beside the tree.

10° near the horizon → 80° high in the sky

02 / Around the horizon

Look down on the shadow

Fixed scale · the outer ring is 30 m from the reference. Pale dot: Sun direction. Gold line: reference shadow.

Shadow bearing
315°

Overhead compass viewShadow and Sun direction, seen from above.NESW

Clockwise from north: N 0° · E 90° · S 180° · W 270°

Follow the light to the ground

The shadow points away from the Sun. Lower sunlight meets the ground farther from the reference, making a longer shadow. Moving the Sun around the horizon changes the shadow’s direction. At a fixed elevation, that rotation does not change its length.

Geometry, assumptions, and sources

In the right triangle, tan(elevation) = height ÷ shadow length. Rearranging gives shadow length = height ÷ tan(elevation).

We model the marked point on an upright 5 m pole beside a tree, using parallel sunlight and level ground. This does not compute a canopy outline, soft edges, slopes, weather, or atmospheric refraction. The two controls are independent experiments, not a real daily or seasonal solar path.

Try the idea somewhere new

If the reference height doubles while the Sun stays fixed, what happens to its shadow length?