Sometimes when we see shadows of objects, the shadows are very sharp and distinct, looking remarkably like the objects themselves. Other times the shadows are "fuzzy" or lacking in a definite edge.

What causes fuzzy shadows?

Under what conditions is a shadow formed in the first place?

In the diagram above we see the requisite pieces. There must be a light source, an object illuminated by the source, and there must be some sort of screen. Various things serve as screens including walls, floors, furniture, etc.

### EXPERIMENTAL RESULTS:

If we experiment with ordinary objects of various sizes and with light sources of various types, we find there are three things that affect the fuzziness of a shadow:

1. Whether the object is close to or far from the screen. Close to the screen, the shadow is more distinct. (Light source to screen distance remains the same.)
2. Whether the light is close to or far from the object. Close to the object, the shadow is fuzzier. Object distance to screen distance remains the same.)
3. Whether the light source is large or small. Larger sources tend to produce fuzzier shadows. (Relative positions of the source, object and screen remains the same.)

### ANALYSIS:

Adjusting the locations of source and screen affects the degree of "fuzziness" of the shadow, and never really causes the shadow to become totally clear. Changing the size of the light source, however, has the ability to change whether there is any fuzziness at all.

CONCLUSION: The size of the light source is the cause of the fuzzy shadows!

### THEORY:

If we could shrink a light source down to a single point, we would find the light traveling outwards in all directions, traveling in straight lines. This is the point we wish you to begin thinking about light - namely that it originates from a single point, whether it's one point or many.

Now if this diverging light hits an object which doesn't allow the light to pass through it (also called opaque), part of the light will be blocked. This forms areas that are lighted, and an area that isn't. The unlighted area is called the shadow.

With light coming from a very small source, the shadow's edges are clear and the shadow is well-defined. The won't be any "fuzziness" if we have a single, small source.

With two point sources, there would be two separate shadows. Where the two shadows overlapped, there can be no light and it would be perfectly dark. Where one's shadow is lighted by the other, the shadow would be an intermediate color or gray. The outside areas lighted by both sources would be light.

The diagram shows what the shadow might look like on a screen, assuming the object is a cylinder held perpendicular to the page and parallel to the screen.

Adding a third source, makes the shadow area more complicated, with areas lighted by all three sources, areas lighted by two sources, areas lighted by only one source, and finally an area unlighted by any source.

As we move from 1 source to 3 sources, the gradations of light at the edges of the central, dark shadow become increasingly complex. When we move to a real source, composed of a very large number of sources, we find the grays blending smoothly together, varying from light to dark gradually. This is the "fuzzy" area, the "fuzzy shadow" that we get when the source has size.

Why are there fuzzy shadows? Because most real sources of light have size: many, many points emitting light, creating many, many shadows, each point helping to fill in the shadows created by other points.

But how do we explain the observations we made during our lab work? In a word, GEOMETRY.

Compare the amount of gray or fuzziness on the three screens at different distances:

At A, the gray, fuzzy area has expanded a little. However, at B, the expansion has proceeded and the area that is fuzzy is now larger. Finally at C, the fuzzy area is at its greatest in this diagram. As the screen gets further from the object, the degree of fuzziness expands due to the geometry of the situation, moving further and further out on a continually increasing triangle.

By moving the source further from the object, the angle is reduced and therefore the amount of fuzziness is also reduced...through Geometry!

### ECLIPSES:

The shadow cast by our moon is a cone-shaped area of complete darkness as shown below. To either side of the cone is a gray area. The completely dark area is called the umbra, while the gray area is called the penumbra. Wherever the moon goes, it carries this dark umbra with it.

Now, as the moon orbits the earth, most of the time the umbra completely misses it. Only on rare occasions does the umbra come close to the surface, and even more rarely does it strike the earth's surface at all. When it does, however we are treated to a special event, a total solar eclipse. The sun will not be seen at all if you are in the umbra as no light can get there. If you are in the penumbra, part of the sun can be seen but not all.

The earth's shadow (due to the sun) is also a cone-shaped umbra surrounded by a penumbra. It is larger than the moon's, though, due to the much larger size of the earth.

In fact, the umbra from the earth is so large that the entire moon can fit inside it. Due to the angle of the moon's orbit and its changing distance from the earth, though, the moon doesn't often cross the umbra in the best possible way. When it does, however, we are treated to a total lunar eclipse.

So other than being fun (like the shadow in Peter Pan), important in all areas of art, and an interesting phenomenon, shadows mostly tell us about the nature of light. Light tends to travel in straight lines and can be blocked by material objects. It doesn't bend around them and fill in the area behind, at least at the scale we are considering here.