Why Does the Inverse-Square Law Fail at Distances Less Than One Meter?

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The inverse-square law, used to calculate radiation intensity, can yield misleading results at distances less than one meter from the source, leading to values that exceed the source's actual intensity. The confusion arises from misunderstanding how the formula applies at different distances, particularly with values less than one. It is clarified that the formula remains valid for all non-zero distances, and the issue is not with the radius itself but with the interpretation of the results. The discussion highlights the importance of correctly applying the formula and understanding the concept of intensity versus power. Ultimately, the original poster resolved their confusion independently.
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I am trying to work out radiation intensity at points along a transect with an increasing distance from the source. Despite having virtually no high school maths, I understand that by applying the inverse-square law (I = P / 4\pir2) to points < 1m from my radiation source is going to give readings which are higher than the intensity of the emitting object, and therefore false.

The embarrassing part is that a) I don't fully understand WHY this is the case and b) I'm not sure how to correct for it. I still need to calculate the radiation intensity at 0.1, 0.25, 0.5 and 0.75m away from the target source. Is there a simple way of correcting it?

This may seem obvious to everyone else, but unfortunately not to me.
 
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The point source is characterized by its power. What do you call "intensity of the source"?
The formula works for all non-zero distances. The radius r=1 does no have any special meaning. I don't see how you come to think that this value (or values less than 1) may be a problem.
 
It was just a question about squaring numbers that are less than one. I didn't mean that the radius was inherently special. Don't worry about it, I've figured it out myself now.
 

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