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Why a Shadow Has Two Edges

About 14 minutes

Put your hand flat against a wall with a lamp behind you. The shadow is sharp — you can see individual fingers with clean edges.

Now walk your hand slowly away from the wall, keeping it in the light. The shadow grows, which you expected. It also goes blurry, which is stranger, because nothing about your hand went blurry.

Draw the outline of that fuzzy shadow with a pencil and you will find you cannot decide where to put the line. There is a definitely-dark middle, a definitely-bright outside, and a band in between that is neither.

Your shadow has two edges, and the reason is not in your hand at all.

Lamps are not points

We draw a lamp as a little dot with rays coming off it, and that drawing is a lie of convenience.

A real lamp has size. A bulb is a few centimetres across. A strip light is longer than your arm. A window is a metre of glowing sky. Every part of that surface is giving out its own light, in its own direction.

So a lamp is not one source. It is thousands of sources, spread out over a patch.

Every part of the lamp draws its own shadow

Take just the top of the bulb. Light from that one spot travels past your hand and lands a sharp hand-shaped shadow on the wall.

Now take just the bottom of the bulb. It also lands a sharp hand-shaped shadow — but from a slightly different starting position, so it lands in a slightly different place.

Two shadows. Same hand. Slightly offset.

One lamp casts two shadows that only partly overlap A tall upright bar stands at the left for a lamp with real height rather than a single glowing point. A small ball sits to its right, and a large wall fills the right hand side of the picture. On the wall are two shadow discs of exactly the same size, one a little higher than the other, because the top end of the lamp and the bottom end of the lamp each throw the ball's shadow to a slightly different place. One disc is filled with lines running across, the other with lines running up and down. Where only one disc covers the wall the shading is single, and a little light still lands there. Where the two discs overlap, both sets of lines cross and the shading is doubly dark, because no part of the lamp can be seen from there at all. A faint dashed line runs from the lamp through the ball to the wall.
The two shadows a single lamp casts, one from its top end and one from its bottom end. Where both cover the wall, no part of the lamp can be seen and the wall is fully dark. Where only one covers it, the other end of the lamp is still shining through.

Now think about a spot on the wall that only one of those two shadows reaches. Standing there, you could look up and still see part of the bulb — the other part is hidden behind the hand, but not all of it. So some light is still arriving. Not full brightness, not full dark. Half-lit.

That is the fuzzy band. It is not blur and it is not your eyes being imprecise. It is a real region where some of the lamp is blocked and some is not.

So the two edges are:

Between them lies the soft band. Outside them, everything is simple.

Why moving your hand changes it

Hold your hand right against the wall and those two offset shadows land almost exactly on top of each other. The soft band is far too thin to notice, so the edge looks perfectly sharp.

Move your hand away and the two shadows drift apart, because their light started from different places and has had further to spread. The band between them widens.

The further the object is from the wall, the wider the fuzzy band.

  1. Switch on one lamp in an otherwise dim room. One lamp only — two lamps make two shadows and that is a different puzzle.
  2. Press one finger against the wall. Look closely at the edge of its shadow. It is sharp.
  3. Draw the finger back a hand's width. Look again. There is now a grey rim.
  4. Draw it back as far as you can while keeping a shadow at all. The rim is now wider than the finger.
  5. Keep the finger still and walk the lamp closer to it. The rim widens again — a closer lamp fills more of the sky, as far as the finger is concerned.
One lamp casts two shadows that only partly overlap A tall upright bar stands at the left for a lamp with real height rather than a single glowing point. A small ball sits to its right, and a large wall fills the right hand side of the picture. On the wall are two shadow discs of exactly the same size, one a little higher than the other, because the top end of the lamp and the bottom end of the lamp each throw the ball's shadow to a slightly different place. One disc is filled with lines running across, the other with lines running up and down. Where only one disc covers the wall the shading is single, and a little light still lands there. Where the two discs overlap, both sets of lines cross and the shading is doubly dark, because no part of the lamp can be seen from there at all. A faint dashed line runs from the lamp through the ball to the wall.

Drag the handle to move the ball towards the wall and away from it, and watch what happens to the two shadow discs.

At the far end the two discs are well apart, so there is a wide band covered by only one of them — a wide soft edge. Slide it down and they close on each other. By the time the ball is against the wall the two discs sit exactly on top of one another, every part of the shadow is crossed by both, and there is no soft band left at all.

Nothing about the ball changed while you dragged. Only the gap between the two shadows the one lamp was already casting.

An overcast sky is the extreme case in the other direction. When the lamp is the entire sky, no spot on the ground is hidden from all of it, so the dark middle never forms and you get soft shadows with no real core — which is exactly why an overcast day feels shadowless.

A photographer wants very soft shadows on someone's face. Knowing what makes a soft edge, what should they do to their single lamp?

What you can now spot

Look at any shadow, indoors or out, and ask two questions. How big is the thing lighting it, and how far is the object from the surface?

A hard-edged shadow means a small light or a close object. A soft one means a wide light or a distant object. Once the two edges are something you look for, you can read the lamp off the wall without ever turning round.