January/February 2017 – Vol. 29 No. 4

The Teaching Length Scale

Posted: Tuesday, May 6th, 2014

by Galen T. Pickett

Physics can be organized by the size and duration of events. When we teach Newton’s mechanics, the examples we use typically are on length scales of meters and on time scales of seconds (tossing a ball, sliding into second base) and run up to solar system scales (tens of millions of kilometers for an Astronomical Unit, and tens of millions of seconds for a year). But, unless your classroom is equipped with technology at the extreme ends of the sophistication scale (chalkboards at the primitive end, and SmartBoards at the super-fancy end), you probably use ordinary whiteboards and erasable marker to make sketches and calculations for your students. The marks you make on this surface meet some basic criteria: they have to be wide enough (half a centimeter or so) to be clearly seen from every vantage in your room and they have to strongly absorb visible light – making a visibly saturated mark. The width of the marks is controlled by the properties of the pen tip, and the saturation of the marks is controlled by the pigment in the marker, but there is another, often overlooked length scale in your markings.

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What is the thickness of the marks? It can’t be zero, and it can’t be on the order of millimeters (you can easily feel roughness on the scale of tenths of millimeters with your fingertips, the width of a single human hair). What I have below can be organized into a demonstration or a full experiment supporting topics in waves and optics.

  • Have a supply of “wet” whiteboard markers on hand. A couple of different colors if you are doing a demonstration, enough for each group to have one if this is a class-wide exploration.
  • Make several marks (or have your kids make marks on their whiteboard slabs), different orientations, curly-cues, some nice cursive if you can manage it, ask for what length scales your students observe.
  • Ask about the thickness of the marks … how far from the surface of the whiteboard do they jut?
  • Use a web-camera and a second light source to show what the marks look like up-close. Make sure you can see the marks “through” the reflection of your light source.
  • If you see other colors … and you will … ask your students if that reminds them of anything. Rainbows, and soap-bubbles, oily sheen are what comes to my mind.
  • What happens when marks “cross” each other? If you press hard when writing, where do you expect the marks to be thinnest?
Pickett_Image1

Figure 1

Here is what is happening. The “green” and “yellow” rays add up “constructively.” (See Figure 1.) That is, they are in constructive interference so you see this wavelength strongly reflected, even if this color were not present in the pigments of the oily marker layer.

The presence of this “rainbow” (see Figures 2 and 3) indicates that there is some interference going on, so the thickness of the marker layer has to be comparable to the wavelength of visible light.

Green light is in the neighborhood of 500 nanometers in wavelength, or 0.5 micrometer. A human red blood cell is approximately a disk of thickness 5 micron, and radius 15 micron, so the marks you use to teach physics are a factor of ten smaller than that cellular scale. When you teach physics, astrophysics, mathematics, history and poetry, you are using one of the great sub-micron teaching technologies of the twentieth century.

Dr. Galen T. Pickett is with the Department of Physics and Astronomy at CSU Long Beach and a member of CSTA.

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From time to time CSTA receives contributions from guest contributors. The opinions and views expressed by these contributors are not necessarily those of CSTA. By publishing these articles CSTA does not make any endorsements or statements of support of the author or their contribution, either explicit or implicit. All links to outside sources are subject to CSTA’s Disclaimer Policy: http://www.classroomscience.org/disclaimer.

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