# Inverse square law radiation protection widget

**Published:** May 25, 2024

**Source:** Design & implementation by Dr Chris Robbins (Grallator) / Facilitated by Ionactive radiation protection resource

#### Prelim

The inverse square law is used in radiation protection (ionising radiation) but is valid for all forms of electromagnetic radiation emitted from a point source. Whilst is can be expressed mathematically, we often tell training delegate to chant (well not quite!) the following:

- Double the distance from a source of ionising radiation - leads to 1/4 of the dose rate (or dose) at the new distance.
- Quarter the distance from the source of ionising radiation - leads to 4 times the dose rate (or dose) at the new distance.

More generally we can say the intensity (dose rate) falls with distance as \( 1/d^2 \), where * d* is the distance from the point source.

Our Ionactive site has some detailed articles on this subject area such as **Inverse Square Law - when is a source a point source** and **When \(1/d^2\) breaks down - part 1: line source**. However the point of this inverse square resource is to keep things really simple. During live training we have taken a balloon and drawn a small square with a black marker pen on the surface (shading to make it as black as possible). Then we have slowly inflated the balloon and imagined that the black square is the intensity (dose rate) of ionising radiation from a point source at the centre of the balloon. As the balloon inflates the surface area expands away from the middle and the square grows larger in area (as \( 1/d^2 \) where * d *is the radius of the balloon - now treated as a sphere). As the square grows the black fades to grey and this represents the reduction of intensity over a larger area - the inverse square law. In the resource that follows black is replaced by dark pink.

This latest resource mimics the idea of the balloon and shows inverse square law interactively.

Enjoy.

**Additional notes**

Each time you load the widget you will be presented with a different reference dose rate (at 1m).

Use the red dot slider to investigate the dose rate at various distances, relative to the initial dose rate at 1m.

Note the attenuation factor, and how this changes with distance (this describes the inverse square law mathematically).

Note how the dark pink square changes with increasing distance (i.e. areas increases, whilst pink intensity fades).