Modeling -- An Introduction, Continued

Now we are ready to experiment with the "shadows" produced by a laser pointer.

Warning: Be very careful -- NEVER look directly into a laser pointer or shine the pointer into your eyes or another person's eyes.

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Shine the laser beam through the pattern on your slide at roughly the point indicated by the red dot in the figure above. Hold the laser pointer and the slide as if you are projecting the slide onto a wall. You should see a "shadow" on the wall something like the picture below. The "shadow" wil be relatively small. It will be larger when the slide and laser pointer are further from the wall. One way to do this experiment is to have one student hold the laser pointer and slide some distance from the wall while other students examine the "shadow" while standing closer to the wall. Be sure to to warn your students not to look directly into the laser pointer.

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We can ask questions about this situation that are similar to the questions we examined earlier with an ordinary flashlight.

Students and most other people are likely to be surprized by these experiments. Moving the laser closer to the slide or further away from it doesn't seem to have any effect on the size of the "shadow." Even worse, the pattern with thinner lines that are closer together produces a "shadow" with the dots more widely spaced than the "shadow" produced by the pattern with thicker and more widely spaced lines. What's going on here"

You may have heard that light behaves like waves in some ways. This situation we are looking at is a situation whose understanding requires an analogy with waves. We will look at a simpler situaion called interference that shows the basic idea involved. You should have a pattern like the pattern shown in the figure below on your transparency film and on the plain paper.

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This picture shows the pattern of waves spreading out from a single light source. Place the transparency film on top of the plain paper so that the two "wave patterns" line up exactly. Nothing surprizing here. But now move the transparency film so that the two patterns don't quite match. You should see what is sometimes called a Moire pattern or, in this case, an interference pattern something like the pattern shown in the picture below. This shows what happens with light from two different sources that are close to each other.

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Move the transparency film around on top of the plain paper. Describe how the interference pattern changes. You are seeing what happens when the distance between the two different light sources varies.

Notice that when the pattern on the transparency film is almost lined up with the pattern on the plain paper the interference pattern has just a few widely spaced light and dark areas. This shows what happens when two light sources are very close together. On the other hand when the pattern on the transparency film doesn't match the pattern on the plain paper as well then there are more, and more closely spaced, bands of light and dark. This is the basic mechanism behind the phenomena we saw with the laser pointer. The laser light going through the pattern on the transparency film acts like light coming through the holes in the pattern and spreading out like waves. These waves interfere with each other creating the patterns we saw on the wall.

It is important to encourage your students to talk with their families about what they are doing in school. One of the attractive features of Web-based materials, like these, is that families with computers and an Internet connection at home can use the same materials their children are using at school. Many families, however, don't have such access at home. The physical apparatus we've been using -- the transparency film and paper with fine concentric circles -- produces striking results that are just plain fun. Students can bring them home to show their families.

Click here to open a new window with a Java applet that simulates three "ripple tanks" -- tanks with water and a way of making waves. Arrange these two wondows so that they overlap and you can move back-and-forth between them by clicking on the exposed portion of the inactive window to make it active. When you are done working with the applet, close its window. This applet can help us understand interference. It has four sections.

You can move the float (the green dot) by clicking at its new location in the right ripple tank. In the right ripple tank move the float to a point where the red and green bands are very strong. Notice what happens to the bar indicating the behavior of the float in the right ripple tank. Now you can see it. Notice that the waves (indicated by the behavior of the floats) arriving at the floats are now "in phase" and as a result they reinforce each other rather than cancelling each other out.

You can move either of the sources by clicking at its new location in either the left ripple tank or in the center ripple tank. What happens when the sources are close together? When they are far apart?

Waves are a wonderful "theme" that can tie students' unify learning from different subjects and different years. For example, when students first learn the Pythagorean Theorem, they can do some wonderful exercises in which they compute the distance from the float in the applet above to each of the two light sources and study the relationship between these two distances and the interference seen at the float's position. Later on, students look at waves when they study differential equations and partial differential equations. This subject arises naturally throughout the curriculum -- at all levels and in many different subjects.

Middle school students can stop here with a first glimpse at one of the big ideas of modern physics -- the wave nature of light -- and bring home the transparency film and plain paper to show their parents and siblings what they did in school. They can talk about or even show what happens with an ordinary flashlight and then they can talk about what they saw in school with the laser pointer shining through very fine patterns. Then they can show their family the striking patterns made when the transparency film is placed on top of the plain paper. If they have a high end computer with Web access at home they can show their parents the applet above.

This is a very open-ended topic, full of chances for further exploration. For example, students might experiment with sound, which also involves waves.

Technology can link students, teachers, and parents in many different ways. Some are low-tech, like students bringing home the transparencies we printed above. But, others make use of two different kinds of modern technology -- network technology and portable technology. As more and more homes are connected to the World Wide Web with browsers and computers that support Java and interactive multimedia, parents will be able to work at home with their children using many of the same resources available at schools. They can even participate with their children and teachers in evening virtual office hours or during regular class time.

Portable technology is equally important. The picture below shows, for example, the Texas Instrument Calculator-Based Laboratory (CBL). Available for well under $200 dollars, this device enables students, teachers, and parents to collect experimental data that can be displayed and analyzed using a computer or a graphing calculator.

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The figure below shows the results of an experiment done with two different microphones recording the sound from a casette tape player. One microphone was further away from the casette player than the other. You can see two effects of the different distances. The sound recorded by the microphone that was further away from the player was not as loud and it arrived at the micorphone later than the sound arrived at the closer microphone. Students can determine a great deal about sound and waves using this apparatus. For example, they can determine the speed of sound and they can determine the effect of distance on volume.

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This is only one of many different kinds of experiments that can be done using the CBL or similar equipment. Because the TI-CBL is flexible, cheap, and portable it can be used by students and their parents at home to do experiments of their own design. Devices like this are replacing more expensive laboratory equipment and giving teachers the new option of sending equipment home with students.

[Next section -- Prolog for a Winter's Day]


Copyright c 1999 by Frank Wattenberg, Department of Mathematics, Montana State University, Bozeman, MT 59717