Poking Fun at Math
Investigate pinholes with a simple viewing device and some colored lights, and collect data to create a real mathematical formula.
- Cardboard tube measuring approximately 2 to 3 inches (5 to 8 centimeters) in diameter and 4 to 7 inches (10 to 20 cm) in length (such as from a roll of paper towels or gift wrap; poster tubes and PVC tubes will also work)
- Aluminum foil
- Wax paper (or a white translucent plastic bag)
- Two rubber bands
- Pushpin
- Red, green, and blue screw-in light bulbs, one of each color (can be CFL, LED, or incandescent)
- Three screw-in light sockets
- Power strip with at least three parallel outlets
- Power source (and extension cord if needed)
- Darkened room
- Partner
- Optional: black construction paper, two additional rubber bands
Build your pinhole viewer:
- Cut the wax paper to a size slightly larger than the diameter of the tube. Do the same with the aluminum foil.
- Cover one end of the tube with the cut piece of aluminum foil, folding the ends over tightly and securing the foil in place with a rubber band.
- Cover the other end of the tube with the cut piece of wax paper, also folding the ends over tightly and securing in place with a rubber band. Make sure the surface of the wax paper is as smooth and wrinkle free as possible; this will be your viewing screen.
- Optional: for better viewing, you may want to add a shade to your screen (wax paper). Roll the black construction paper around the wax paper end of the tube, leaving the foil end exposed by a few inches (10 cm). Secure the construction paper in place with rubber bands.
Put together your light source:
- Screw the red, green and blue bulbs into the light sockets.
- Plug one, two, or three bulbs into the power strip and turn it on.
Use the worksheet provided to collect and record data from the following experiments:
Use your pushpin to poke a single hole anywhere in the foil on your viewer. Turn on one light (of any color). Hold the viewer up to the light, with the foil side oriented towards the light, and look at the image on the wax paper. Record your data. Turn on a second light, and then the third light. How many images do you see?
Poke a second hole in your foil and hold it up to the light, again starting with only one light on, then two lights on, then all three lights on. Record this data.
Continue poking additional holes in the foil. For each new hole, test the viewer against different numbers of lights, and record your observations as you go.
Do you see a pattern in the data? What is the relationship between holes, bulbs, and images? Based on that relationship, make a prediction: if you know the number of holes poked and the number of bulbs, how many images will appear? Can you represent this as a mathematical formula?
You’ve created a pinhole image multiplier! The number of images on the wax paper is related to the number of pinholes and the number of bulbs:
$$\text{bulbs}\times\text{pinholes} = \text{images on screen}$$
Light rays travel in straight lines and in all directions from a light source. However, your pinhole device limits the rays that can reach the wax-paper screen. The aluminum foil blocks all the light except that which passes through the pinhole(s).
Because the red, green and blue bulbs are in slightly different positions relative to a given pinhole, the light from each bulb reaches that pinhole at a different angle, making a "set" of one red, one green, and one blue image, each in a slightly different position on the screen. Each additional pinhole you create (because it's in a different position and light passes through it at different angles) creates another set of red, green and blue images. (Click on image to enlarge.)
You may notice some interesting color effects in the places where the images overlap on the screen. To explore those, try Poking Fun at Color Mixing.
Another math activity you can do with this Snack is to investigate the relationship between the distance from the viewer to the light source and the size of the image of the light source on the wax paper screen. You can collect data to discover the mathematical relationship between these variables.
