Radiation and the Inverse Square Law

Direct students to the Explore section of the Measuring and Graphing Light handout.

Display slide 9. Point out that flashlights are a model of the Sun (and other radiating sources). Demonstrate measurement of the radius of a light circle, pointing out that the outer radius should be measured and recorded in Column 2. Direct students to take all measurements and finish Column 2 before moving onto the calculations of Columns 3–5.

Display slide 10, which summarizes the workflow of the Explore phase. Use it to orient students to the objectives of the activity before and during the activity.

Put students into groups and ask them to start working. Groups of 2–3 are optimal. Larger groups may inhibit individual student engagement.

Follow these tips to help ensure that the activity runs successfully:

1. Room Lighting:

   Darken the room as much as possible so larger, dimmer light circles can be perceived and measured. Encourage students to measure all of the light circle radii first while the room is dark. Then, when all groups have their measurements, turn the room lights back on to catalyze calculation work.

2. Surfaces may be vertical or horizontal, but must be of sufficient size:

   The flashlight is held perpendicular to the surface. It does not matter if the light is directed down onto a horizontal surface (desk, floor) or from the side onto a vertical surface (chalkboard, wall). However, the surface needs to be large enough to contain the largest light circle. Thus, lab tables and floors work better than desks.

3. Measure the outer cone of light:

   The outermost cone of light from a flashlight usually follows the inverse square law better than inner features. Demonstrate measuring the outermost ring of light (and point out the direction in the handout) to reinforce this tip.

4. Checking and helping with calculations:

   Column 3 converts radii measured in cm (Column 2) into meters. This step makes the brightness results in Column 5 larger and thereby easier to understand and graph. Column 4 is calculated using Column 3 (not Column 2) radii using the equation for circle areas (A = pi*r*r). The values in this column should be small numbers (usually <1) that increase as you go down the column. Column 5 is calculated as 1 divided by AREA, and values should decrease moving down the table. Depending on the class's familiarity with quantitative work, you may need to demonstrate a row of calculations to a group or the whole class (use slide 9). Be ready to show students how to use of the "1/x" button on their calculator to turn Column 4 area into Column 5 brightness.

5. Checking graphs:

   Graph A (light radius vs. distance from the surface) should be a linear graph that looks like Graph D in the handout. Graph B (light brightness vs. distance from the surface) is an inverse square relationship that looks like Graph C in the handout. Make sure students label their axes and appropriately space numerical values along the axes (less experienced graphers often use even spacing for unevenly distributed values).

6. Time management:

   Depending on the time invested in the Engage, the length of your period, and the students' comfort with calculations, students may need time at home or at the start of the next class to complete the calculations and graphing steps.