Inverse square law

Last revised by Raymond Chieng on 5 Aug 2023

The inverse square law describes the principle of dose reduction as the distance from the source increases.

This assumes a point source. The source can be considered as a "point" source if the distance is more than 7 times the dimensions of the source 4. The radiation will spread equally in all directions over a spherical area. As the radius increases, the area over which the dose is distributed increases according to

A=4πr2

where A is the area and r is the radius of the sphere.

Therefore, the dose is proportional to the inverse of the square of the radius. Thus doubling the distance will reduce the dose by a factor of four.

Applications

In fluoroscopy, there should be a minimum distance between the X-ray tube and the patient of about 30 to 38 cm to reduce the skin entrance dose of the patient. Meanwhile, the image intensifier (which intensifies the X-ray photons to produce a bright image) should be as close to the patient as possible to reduce image blur and maintain the brightness for the image intensifier, thus reducing the patient's dose. If the image intensifier is too far away from the patient, the brightness output will reduce. Meanwhile, the automatic brightness control (ABC) will increase the X-ray tube output to increase the brightness, thus causing increased dose to the patient 6.

When not dealing with radiopharmaceuticals, standing 6 feet away can reduce the radiation exposure to 2.8% when compared to the radiation dose when standing at 1 foot away from the source 4.

Using tongs or long-handled tools when handling radiopharmaceutical products can increase the distance of the source from the handler, thus reducing radiation exposure 4.

Inverse square law is used in the calculation of the geometric effectiveness of collimators used in nuclear medicine 5.

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Cases and figures

  • Figure 1: inverse square law
    Drag here to reorder.