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

[TreeScience]

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$\pi$r²) 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.

 

[nasu]

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.

 

[TreeScience]

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.