Not many people give much thought to crystal balls (or as scientists call them: spherical lenses), but crystal balls have more uses than one would initially think. My project began after I read an article about a crystal ball starting a small fire in a house. The ball was left on the couch, and as the sunlight came in through the window, it was focused through the ball and began a fire on the couch. Fortunately, this was soon put out by the fire department. This situation was related to my interest in forensics, bringing up questions of the actual circumstances of the fire, and if it had really occurred as said.
Once my interest in crystal balls was developed, I did some research about the uses these lenses have had in scientific history. I found out that it was through a simple glass bead that Leeuwenhoek discovered the microscopic world. Leeuwenhoek was a fabric merchant, using small "glass pearls" to study the fabric quality more carefully. Unlike other fabric merchants, he was increasingly interested in studying other things under the magnification of the glass beads. Throughout this technique he started studying other materials, most frequently pond water. In order to look at subjects under increasing magnification, he used beads with smaller and smaller diameters. This worked well, but as the beads got smaller, he found them hard to work with, and ended up creating a mechanism to hold the beads at a specific distance from the subject. This was the first simple microscope.
To find out more about Leeuwenhoek's microscope, check this web site.
These pictures show some small crystal balls that Dr. Noe ordered from the Edmund company, and illustrate how they magnify.
Once I had some background information, I decided to focus my project on figuring out if the "crystal ball fire" was possible, and what the circumstances must have been for the fire to start.
Testing the Magnifying Glass
I began by testing the burning power of a regular magnifying glass, since a crystal ball or spherical lens is just a variation of the simple magnifying glass. When a magnifying glass is held a distance exactly equal to its focal length above a piece of paper, the sun's rays are focussed to a small very hot spot. I practiced finding the focal length, and found that in order to set an actual fire, it was necessary to darken the paper with a pencil. This is because the dark color will absorb more energy, while the bright white printer paper reflected too much light. With the strength of the sun that day, as well as the magnifying level of the lens, a fire could not be started without filling in the spot with a pencil.
Testing the Crystal Ball
I used a crystal ball with an 11 cm diameter to try to simulate some of the conditions in the "crystal ball fire." First, I placed the crystal ball directly on a piece of cardboard. Cardboard was chosen as the medium since it has a darker color than printer paper, and is relatively easy to set on fire. I placed the ball directly on the cardboard since it was assumed that the crystal ball in the article was lying on the couch.
When placed on the cardboard, the crystal ball was not a full focal length away. This would cause the focal point to not become as hot since the rays are not at their full focusing capacity. It was easy to see that the spot was larger than it would be if the the crystal ball was a full focal length away, being more spread out. The ray of light on the cardboard was 1.9 mm. The light rays could be seen coming through the cardboard, but the spot was not nearly hot enough to set a fire.
This conclusion was surprising, considering the crystal ball in the article was supposed to have been resting directly on the couch. I realized that there were other circumstances that might have been present for the "crystal ball fire" to be possible.
The next thing that I tested was the burning ability of the crystal ball on printer paper when it was exactly one focal length away. The approximate focal length could be found through trial and error, this distance being whenever the crystal ball produced the dot of light that was smallest and brightest.
Through this exercise, it was obvious that a fire could be started on this material if it was darkened by pencil lead, similar to the results found with the magnifying glass. The paper would set fire within a few seconds when the crystal ball was right distance away.
Understanding the Focal Length of a Sphere
There are two ways to describe the focal length of a sphere. The Effective Focal Length (EFL) is the distance from the center of the sphere to the focal point, while the Back Focal Length (BFL) is the distance from the exit surface of the sphere to the focal point. The EFL and BFL are both proportional to the radius, and depend only on the index of refraction (n). In other words, a sphere with identical index of refraction that is twice as big will have a focal length that is twice as large as well.
The two focal lengths can be calculated from these equations:
BFL/R = EFL/R - 1
Here is a plot I made from these equations using a spreadsheet. It shows that for an index of refraction of exactly n = 2.0 the focal point is at the exit surface of the sphere (BFL = 0). This is an important fact when designing retroreflecting materials.
Plot of EFL (solid blue line) and BFL (dotted red line)
Regular glass has an index of refraction n of approximately 1.5, but "crystal glass" has an index closer to 1.75, depending on the exact material. I decided to test what kind of glass this sphere actually was by measuring its index of refraction.
First, I measured the Back Focal Length by holding the crystal ball under overhead lights directly over a piece of white paper. I varied the distance from the sphere to the paper until the image of the lights was in sharp focus. At this point I measured the distance from the paper to the bottom of the crystal ball. After making a small (5%) correction to account for the lights not being infinitely far away, the result was a BFL of 2.2 cm. Since the sphere has a diameter of 11.0 cm, the radius is equal to 5.5 cm. This means that the BFL/R equals 0.400. From the equations and the plot above, the index of refraction of this particlar crystal ball was thus found to be 1.556 +/- 0.010. This value is significantly higher than ordinary glass (n = 1.52) and a little lower than "light flint glass" (n = 1.58), as explained on this web page.
These experiments taught me more about focal lengths and magnification, but what this whole project was about was learning more about the exact conditions that must have been present at the "crystal ball fire." I came to realize how much physics is necessary to solve seemingly simple problems such as whether a fire could have possibly started based on a theory of where it was and how it began. These facts showed me that light is focused very quickly in a crystal ball, and if the couch is dark and made of a certain material, it ws probably very easy for the fire to start. Although the crystal ball could not have been a focal length away if it was directly on the couch, it was possible that it was placed on a crack between two cushions, allowing space in between the material and the ball. This is one theory, but the second, and more likely one, is that the fire started late in the day when the sun was low in the sky. The angle of the sun at this time would cause there to be a gap between the ball and the flammable surface, so that the sunlight falling on the surface would create a tiny, very hot, spot. In this way, it is definitely possible for the fire to begin, and in order to be positive, specific conditions must be known.
Above all else, this project showed me that a knowledge of physics is needed to solve even the most everyday problems. Even in a field such as forensics, which is associated so much with biology, physics plays an integral role in re-enacting crime scenes. Something as simple as understanding the "crystal ball fire" involved a lot more physics and math knowledge than most people would ever expect.