Activity to Teach the Inverse-Square Law for Radiation Flux

Context: • This activity is used in a 300-level course on Earth Systems

and Environmental Science (using Kump, Kasting, and Crane text), but could be used in an intro class, as well.

• This is used at the beginning of a section on Energy Balance.

• We just covered electromagnetic radiation and now are beginning a section on radiation flux.

Objectives:• Students will be able to demonstrate how the inverse-square

law for radiation flux works.• Students will be able to define terms in the inverse-square

law and apply this law to an example problem.

Radiation Flux

What do I mean by the term “flux” ????- rate of energy or material that passes through a

given area over a period of time- flux of water in a reservoir may be given in

m3/day (volume per unit time)

We cover what “radiation flux” is after covering the electromagnetic spectrum:

figure 3-4DEMO...

Radiation FluxGetting to the concept of flux per unit area:

Radiation FluxHow much flux does Venus get

versus Earth? Mars?To answer this, how might you go about estimating radiation flux to these different planets (assume you can measure flux on Earth, which we can!)?

Which planet do you think will have greater radiation flux? Why?

• What parameters might be critical to understand from this concept?

• Can you write a functional equation that captures this concept [e.g., y = f(x)]?

Activity:•With the flashlight, ruler, and a piece of paper, do the following:

1. Shine the flashlight on your paper from 5cm distance (call this r0). Measure the diameter of the resulting spot of light.

2. Do the same using the light source 10cm distance (call this r).

3. Assume that the energy from the light is 100 units. Calculate how much ‘energy’ per unit area is received at the paper for each distance (call the value for 5cm distance, S0 and the value for 10cm distance S).

4. Take the ratio of these numbers .

5. Next, play with different ratios of your distance from the paper (r0 and r) and see if you get a number that is close to the ratio of energy.

0S

S

Inverse-Square Law

So = energy at referenceSurface area of sphere = 4πr2

Rearrange this equation to put the different ratios on opposite sides. Is this close to your equation?

NOTE: Energy from the Sun is released in a spherical pattern, so the geometry of the system is 3-dimensional while yours is 2-dimensional.

Radiation Flux

How much flux does Venus get versus Earth? Mars?

Inverse-Square Law

Distance from Sun: Venus: 0.72 AU Earth: 1.00 AU Mars: 1.52 AUEarth Flux: 1370 W/m2

What is flux on Venus and Mars?

So = energy at referenceSurface area of sphere = 4πr2

Radiation FluxHow much flux does Venus get

versus Earth? Mars?Distance from Sun: Venus: 0.72 AU Earth: 1.00 AU Mars: 1.52 AUEarth Flux: 1370 W/m2

What is flux on Venus and Mars?

Venus:

Mars:

22 W/mW/m 264372.0

00.11370

2

AU

AUS

22 W/mW/m 59352.1

00.11370

2

AU

AUS