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Episode 315: The inverse square law

This episode considers the ways in which the intensity of radiation decreases with distance from the source.


  • Demonstration and discussion: radiation spreading out, and an analogy. (20 minutes)
  • Worked example: Thinking in proportions. (5 minutes)
  • Student experiment: Estimating the power output of the Sun. (15 minutes)
  • Student questions: Comparing lamps. (30 minutes)


Demonstration and discussion: Radiation spreading out and an analogy
Set up three simple demonstrations:

  • Bright lamp and phototransistor or other light meter
  • Microwave source and detector
  • Gamma ray source and Geiger counter


Show that the intensity of each type of radiation decreases with distance from the source.

(If students have already studied radioactivity, they may be aware of the inverse square law for gamma radiation.)

Why does the intensity decrease with distance? Try to give two general reasons. (Absorption and spreading out.)

Radiation spreading out radially covers a bigger and bigger area, proportional to r2, so its intensity decreases as 1/r2. It can help to think of a ‘toast-buttering gun’. The gun can butter a single slice of toast at a distance of 1 m. How can it butter four slices simultaneously? (Place them in a 2 × 2 array at a distance of 2 m.) How thick will the butter be? (1/4 of original thickness.) Extend this to a 3 × 3 array at 3 m, and so on.

Point out that the intensity of radiation can be measured in watts per square metre (W m-2).

Worked example: Thinking in proportions
A cobalt 60 source gives a gamma dose rate of 160 μSv h-1 at 1.0 m away. At what distance will the dose rate be

40 μSv h-1?

Answer: If the intensity has gone down by a factor of 4, the distance away must have doubled to 2.0 m.

Or by I = k/d 2so I 1 /I 2 = d 2 2 /d 1 2 .

Student experiment: Estimating the power output of the Sun
Students can make measurements to estimate the power output of the Sun, making use of the inverse square law. Note that there is a good opportunity here to discuss the validity of the answer obtained.

TAP 315-1: Summer Sun remembered

Student questions: Comparing lamps
Some calculations.

TAP 315-2: Comparing intensities for lamps

Download Word version of Episode 315 (77 KB)

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