(15 minutes or less)
Before you buy large quantities of transparent tape, test the brand you are buying by placing a strip of the tape between two pieces of polarizing material. For convenience, you can actually stick the tape to one of the polarizers. Then rotate one of the polarizers against the other. If the tape changes from dark to light, or vice versa, when you rotate the polarizer, you can use the tape in this recipe. If the tape remains the same shade of darkness when you rotate the polarizer, the tape will not work in this Snack.
We make our patterns on glass or Plexiglas™ because these materials add no color to the design. Most plastic will not work as a backing material, since it produces colors in this situation. However, we have found that the transparent plastic tops of greeting card containers can be used successfully.
Put strips of tape on the piece of glass or Plexiglas™ in a crisscross or random pattern. Be sure that there are several areas where two or three strips of tape overlap and crisscross. Sandwich the glass between the polarizers; then place the resulting package on the overhead projector. Rotate the top polarizer and observe the color changes.
You can also use multiple layers of crisscrossed tape to create pictures. The tape can be cut as necessary so that it forms the desired shapes. You can also form letters and words.
The colors that you see result from differences in the speed of polarized light as it travels through the transparent tape. In transparent tape, the long polymer molecules are stretched parallel to the length of the tape. Light polarized parallel to the stretch of the molecules travels through the tape more slowly than light polarized perpendicular to the stretch. (For an explanation of polarization, consult the Polarized Sunglasses Snack.)
Every material has an index of refraction - that is, the ratio of the speed of light in a vacuum to the speed of light in the material. Light travels through the tape you used in this demonstration at two different speeds. (Materials with this property are called birefringent, which is derived from the Greek words for "doubly refracting.")
When polarized light enters the tape, its direction of polarization will probably not line up with the length of tape. If the light is polarized in a direction that does not line up, its direction of polarization will be resolved into two perpendicular components. One of these components will be parallel to the length of the tape, and one will be perpendicular.
The waves that comprise these two components are initially in step with each other. But as they travel at different speeds through the tape, they become out of step. That is, the crest of one wave no longer lines up with the crest of the other. When these out-of-step light waves emerge from the tape on the other side, they recombine, making light with a different polarization than the original light's.
The thicker the tape is, the more out of step the components will become, and the greater the change in the polarization will be. If, for example, the two waves recombine after one has been delayed by onehalf a wavelength, the direction of polarization of the light will be rotated by 90 degrees.
The white light shining from the overhead projector is made up of light of all different colors or wavelengths. Since the index of refraction of the tape is different for each color of light, each color has its own unique pair of speeds as it passes through the tape. The result is that the polarization of each color is changed by a different amount for a given thickness of tape.
When a second piece of polarizer is placed over the tape and rotated, it transmits different colors at different angles. This accounts for the color combinations that you see at a given angle, and for the changes in color as the polarizer is rotated.
This diagram is similar to one found in Paul Hewitt's excellent book, Conceptual Physics (seventh edition, HarperCollins College Publishers, New York, 1993).
For more information, two excellent references are Hewitt's Conceptual Physics, and Seeing the Light by David Falk, Dieter Brill, and David Stork (Harper & Row, 1986, pp. 358-365).
You can adapt this technique for use with a 35 mm slide projector. Punch the film out of an old 35 mm slide and crisscross layers of tape over the opening. Place a piece of polarizing material inside the projector just in back of the slide and rotate a second piece in front of the lens. As the front polarizer is rotated, your creations will change colors. Colors are determined by the orientation of pieces and thickness of the layers. Rotate the polarizer to the rhythm of your favorite music, and you will have a creative, do-it-yourself light show.