Colored Shadows: no illusions, just physics and biology
Look at the picture above. What do you see? Maybe the shadow of a building with some colored windows. Perhaps it is a student’s art project, a painting of some type. What if I told you it isn’t a painting at all and that the color is all due shadows from different colored light bulbs? Seems impossible doesn’t it, shadows that are colored instead of black. What if I also told you that despite there being at least five distinct colors in the picture, only three colored lights are needed. What is going on?
Let’s first start with what is a shadow. A shadow is simply the result of an object blocking a light source, which is why your shadow appears on the opposite side of your body as the Sun is. Since most of the light we encounter comes from a single source like the sun or a lamp in a room, we only have one shadow. But if there are multiple light sources, there is also a shadow from each of the light sources. So in the picture, since there are three lights (a red one, a blue one, and a green one), there should be three shadows.
But what about the colors: if there are three light sources and three shadows, shouldn’t there be only three colors in the shadow? Yes, there should only be three colors, but the fact that we see more is due to how our eyes perceive color. In art class, you may have learned that the three primary colors are red, blue, and yellow and by mixing these colors, you can get all of the other colors.
The reason we can mix colors is that the colors of objects are determined by the color of light they reflect to our eyes; all of the other colors are absorbed by the material. So if your shirt appears yellow, it is because yellow light is reflected from your shirt while all the remaining colors are absorbed by your shirt. This is also why wearing a dark-colored shirt can make you feel warmer than wearing a lighter colored shirt on a hot day.
While this explanation of color is good enough for describing the color of objects, it is missing a few details to explain what happens when mixing lights of different colors. Even though I said the primary colors are red, blue, and yellow, I used a red, blue, and green light. The reason for using a green light instead of a yellow light is a result of how the human eye sees color. To perceive color, the eye has specialized cells, called cones, which respond to specific colors of light, which turn out to be primarily red, blue, and green. Depending on which of the three types of cone cells is triggered, you will see different colors. Any color you observe outside of red, blue, and green is the result of multiple cells responding. For example, when the yellow light is reflected from your shirt, the cones corresponding to red and green light are triggered, which means your brain cannot tell the difference between yellow light and red and green light entering your eye at the same time. Hence, if a red light and a green light shine on the same spot, you will see a yellow spot rather than a red spot and a green spot.
Now we can explain why we see more than three colors. Since there are three lights, there will be three shadows. However, not all the lights are blocked at each point on the wall. For example, when only the blue light is blocked by the object, the red and green light still reach the wall behind the object. But because your eye perceives red and green light at the same place to be yellow, you see a yellow shadow. Likewise, when only the red light is blocked, the blue and green light still reach the screen so we see a cyan shadow. If two of the lights are blocked though, we will only see the remaining color. Since there are three ways to block one of the lights and three ways to block two of the lights, there six total ways to block the lights and hence six possible colors of the shadows, 5 of which we observe (the sixth is not seen since there is no place where only the green light is blocked). In the image below, the paths of the light are traced to show how this works. So what may have seemed to be an illusion or some complicated set up turned out to be nothing more than a simple consequence of physics and biology.