We don't usually notice shadows but they are everywhere.  Sometimes they work for us (the shade under a beach umbrella is a welcome escape from the heat of the sun).  Sometimes they are a nuisance (it's hard to read when a shadow is cast across your book).  A lot that is done to illuminate the home, the workplace, or the sports arena is an attempt to eliminate shadows, and yet we plant trees and install drapery and awnings to make shadows.

We begin the study of light with shadows, because they are easily observed and lend themselves well to prediction, measurement and data analysis.  They have a behavior that is not entirely simple but which can be completely understood knowing that light travels in a straight line.  Although this seems to be a simple concept, its implications are deep and affects practically everything we see.  Also, understanding and predicting where light will go and what the result will be is a necessary tool for understanding other important concepts such as reflection and refraction.

Applications of shadows

The X-ray images of teeth, bones, and the contents of your carry-on bag are shadows, made by a kind of light that goes through most things, but is scattered more by dense materials such as metals.

A sundial is a way to measure the position of the sun (and thus determine the time) by observing its shadow.

The first measurement of the size of the earth was based on the length of shadows exactly at noon in different places. For the shadow lengths to be very different, you have to go north a significant fraction of the radius of the earth. Observing the shadow lengths allows the size of the earth to be calculated.

During an eclipse of the sun, we are briefly in the shadow of the moon; during an eclipse of the moon, it is passing through the earth's shadow. The duration of the eclipses was one of the first hints to early astronomers that the moon is smaller than the earth (but not a lot smaller) and that its distance from earth is about 100 earth-diameters -- much less than the distance to the sun.

There is another kind of astronomical shadow that played an important role. About every 100 years, the planet Venus passes directly in front of the sun, so that it appears as a small dark region on the sun's disk. From different places on the surface of the earth, we get different views, and the path of Venus across the sun's disk is slightly different.  This provided the first way that astronomers could measure the distance from the earth to the sun.  The reason that Captain Cook sailed to the South Pacific (accidentally discovering New Zealand on the way) was to make a measurement of the transit of Venus that occurred in 1769.

Have you ever wondered how big a cloud is? You can tell, by looking at its shadow. All you need is a vantage point from which you can see a large field, like a tall building or a scenic overlook on a mountain road, or the view from an airplane window. The shadows are huge! Even the little puffy clouds of a summer afternoon have shadows that are most of a kilometer wide.

But don't we have to correct for the fact that the clouds are closer to the sun?

The answer

Everyday shadows

Our shadow dutifully follows us around, and we hardly ever notice it.

Sometimes it looks funny (for a discussion, go here).	---------	Sometimes we have more than one!

If you sit in the window seat in an airplane, you can look for the shadow of the airplane on the ground. The shadow should be about the same size as the airplane -- about as big as a barn. Barns are hard to see from several miles up, too. However, the shadow of the plane is also hard to see because it is fuzzy. That's because (as we found out with the flagpole) the sun looks like a disk, not a dot, and the beams of light coming from the top and bottom edges of the sun are travelling slightly different directions. The effect becomes more prominent as the object making the shadow gets farther from the surface on which the shadow is cast. When the airplane is miles high, the shadow is very fuzzy and hard to see.

However, you will see something else: the ground is slightly brighter right where the airplane shadow is supposed to be! The reason for this is that you are looking right along a sun beam, and from this point of view you cannot see the shadows that objects on the ground cast behind them -- you see only their brightly illuminated front side. In the sketch, the people in the airplane cannot see the shadow on the back side of the hill. This effect is most prominent when the surface is rough, so that there are lots of shadows.  (This is also the explanation why the full moon is very much brighter than at other phases.)
A shadow puzzle

Sally's shadow is sharp, and the lamp post shadow is fuzzy. Why?

The shadows unit