Inverse Square Law

As we've learned so far, the ALARA principle is an important thought process that X-ray operators should practice.  If practiced properly, dose is lowered for the workers, patients, and public.  Within the ALARA principle, we have the 3 Cardinal Principles of Time, Distance, and Shielding.  The inverse square law deals with distance.  For the worker, distance can be your best friend when around radiation sources.  The Law states "The intensity of the radiation is inversely proportional to the square of the distance"

In simpler terms, every time you double your distance from the source of radiation, you cut the intensity of that radiation by a factor of 4!  For example, let's say we measure an intensity of 100 mR when you are 1 foot from the radiation source...

Distance measured at 1 foot = 100 mR

Distance measured at 2 feet = 25 mR

Distance measured at 4 feet = 6.25 mR

You can see from the example above that distance is your friend.  Standing 1 foot away, you measure 100 mR.  Increase your distance to 2 feet, and the intensity drops to 25 mR (which is 1/4th the intensity of 100 mR).  Take that 25 mR at 2 feet and double your distance again to 4 feet, the intensity drops to 6.23 mR (which is 14th the intesity of 25 mR at 2 feet).  So what started as 100 mR at 1 foot away become 6.25 mR by the time you are 8 feet away.


So why does this happen?

If you take a flashlight and shine it 2 feet from a wall, you'll notice the light pattern on the wall is a certain size.  If you keep the flashlight shining on the wall while increasing your distance from the wall, you will notice the size of the light pattern increase.  If you double your distance to 4 feet, the area of the pattern is actually 4 times bigger.  This is due to divergence of the beam, meaning as the light beam travels, it spreads.  Since you have the same number of photons spread over a larger area, the intensity of the beam is less.  This is exactly what happens to x-rays as well.  So how do we calculate it?


 The formula for the Inverse Square Law is Old Intensity over the New Intensity equals New Distance Squared over the Old Distance Squared.  You write down the formula and then determine what the old intensity is, the old distance is, and what the new distance is.  Then it is just a matter of plugging in the numbers and calculating.
inverse square law
"I" is the intensity of the x-ray beam.
"D" is the distance SQUARED.  It is very important to remember squaring the distance.
Let's try the example below:

If a LXMO stands 1 meter from the x-ray tube and receives an exposure of 2 mR, what would the exposure be if the LXMO moves 2 meters away?
inverse square example