# Radiation and the Inverse Square Law

## Electromagnetic Radiation, Astronomy, and the Inverse Square Law

Lindsey Link, Matthew Peck | Published: June 14th, 2022 by K20 Center

• Grade Level 8th, 9th, 10th, 11th, 12th
• Subject Mathematics, Science
• Course Chemistry, Earth Science, Geometry, Physical Science, Physics
• Time Frame 1-2 class period(s)
• Duration 100 minutes

### Summary

Students will establish the relationship between radiation intensity and the distance of a radiating source using a simple flashlight model. Students will learn to apply the inverse square relationship to consider the effects of a planet’s distance from the Sun on its ability to be colonized and adapt the inverse square law to charge-charge and gravitational attraction forces and other situations.

### Essential Question(s)

How does the intensity of radiation change as the distance from the radiating object changes? How does this relationship help us find planets for human colonization?

### Snapshot

Engage

Students select and share their ideas for a planet or moon in a solar system that humans could colonize. Next, students take T-Chart notes while watching a video on Mars colonization. Follow-up questions engage consideration of solar EM radiation in colonization.

Explore

Students use flashlights as a radiation model to measure the relationship between the distance from a surface and the brightness of a light circle. Students measure light circle radii, use geometry to calculate the light circle areas and brightness, and make two graphs to visualize data.

Explain

Students explain how the light circle radius, area, and brightness depend on the distance of a light source from a surface. They analyze graphs to describe relationships as "direct" and "inverse." They explore the equations and geometry behind brightness' "inverse square law" relationship.

Extend

Students apply flashlight logic and the inverse square law to radiation in the solar system. The inverse square law is extended to charge-charge attraction, gravity, and other situations.

Evaluate

Students watch a second video, which considers colonization of Venus. Students use evidence from the lesson (including the two videos) to write a letter to the President advocating for colonization of Mars, Venus, or an alternative solar system body.

### Materials

• Measuring and Graphing Light (attached; 1 per student)

• Measuring and Graphing Light (Teacher's Copy) (attached)

• Lesson Slides (attached)

• Flashlights (1 per group of 2–4 students)

• Meter sticks (1–2 per group of 2–4 students; rulers could be substituted)

• Calculator or phone with calculator app (1 per group of 2–4 students)

• Lab notebook (optional)

• Pencil or pen

• Sticky notes (1 per student)

### Engage

20 Minute(s)

Before you begin, pass out a copy of the attached Measuring and Graphing Light handout to each student. Use the attached Lesson Slides and Measuring and Graphing Light (Teacher's Copy) handout to guide students through the lesson. Briefly review slides 2–4, introducing the lesson title, Essential Questions, and Lesson Objectives.

Direct students to the Engage section of the Measuring and Graphing Light handout. As you go through the next few slides (with instructions below), have students record their answers either in their lab notebook or on the handout, depending on your preference.

Display slide 5. Hand each student a sticky note (or have them use paper or an electronic submission form) and have them write a response to the question on the slide: "What planet or moon in the Solar System (excluding Earth) would be the best place to build a human colony?" As prompted by slide 5, direct students into pairs to share their answers and rationale. Using the instructional strategy Affinity Process, ask them to combine two groups to form a larger group and repeat the process. Finally, have them post their answers to enable all classmates to view the variety of answers. Many students are likely to suggest Mars, which segues into the video shown next.

Display slide 6. Introduce students to the video "Can We Colonize Mars?" Depending on your preference, have students watch the video as a class or individually. Direct students to use a T-Chart to take notes on the reasons for—and challenges surrounding—the colonization of Mars.

Ask students to spend a few minutes answering Engage questions 3–6. Questions 5 and 6 set up hypotheses for the Explore phase. Ask them to answer questions individually or with an Elbow Partner. Then, display slides 7 and 8 to discuss answers briefly. Expected answers and clarifications are in the Measuring and Graphing Light (Teacher's Copy) handout.

### Explore

20 Minute(s)

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.

### Explain

20 Minute(s)

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

Display slide 11. Show students that Graphs C and D are in the Measuring and Graphing Light handout and are used for answering Explain questions. Have students answer questions, either individually or in small groups, before discussing answers as a whole class. Questions 1–6 directly relate to the lab data and involve relatively simple comparisons with Graphs C and D. Questions 7–9 address algebraic and geometrical considerations that are more difficult for some students to answer independently.

Display slide 12 to discuss Explain questions 1–6. Sample answers and clarifications are in the Measuring and Graphing Light (Teacher's Copy) handout. Slide 12 is animated to circle the correct relationships. Go back to slide 11 to visually reinforce the similarities between Graphs A and D and between Graphs B and C.

Display slide 13 to discuss Explain questions 7–9. It contains an animation of similar triangles that help students visualize the linear relationship between horizontal distance from a surface and the vertical radius of the light circle.

### Extend

20 Minute(s)

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

Direct students to work on the questions on their own (or in small groups). Students will need or want to research details for a complete understanding of questions 3–6.

After students have worked on the Extend questions, use a Gallery Walk to have them report out in small groups and/or run a class discussion using slides 14–16 as visual aids. Sample answers and clarifications are in the Measuring and Graphing Light (Teacher's Copy) handout.

Display slide 14 to review Extend questions 1–6, which apply the flashlight activity logic to the solar system and the search for planets that could support life.

Display slide 15 to discuss Extend question 7. To further demonstrate the inverse square law and the importance of small distance changes making larger brightness changes, move around the room with a flashlight to show students how brightness changes depending on how far the light is from the students.

Display slide 16 to discuss Extend questions 8–10, which apply the inverse square law to situations beyond light.

### Evaluate

20 Minute(s)

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

Display slide 17. Introduce students to the video "Should We Colonize Venus Instead of Mars?" Depending on your preference, have students watch the video as a class or individually. Direct students to use a T-Chart to take notes on the reasons for—and challenges surrounding—the colonization of Venus. The video is about 8 minutes long.

Display slide 18 and go over instructions for writing a persuasive letter to the US President advocating the colonization of Venus, Mars, or a solar system alternative. Decide how much time students will have to do additional research and write their letters. Depending on your preference, have students work on this task in class or as homework. Having students write letters in groups is not recommended.