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

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In summary, the person is trying to calculate radiation intensity at different distances from the source, but is unsure about how to correct for false readings at distances less than 1m due to the inverse-square law. They are seeking a simple solution to this issue.
  • #1
TreeScience
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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[itex]\pi[/itex]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.
 
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  • #2
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.
 
  • #3
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.
 

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

What is "The square of less than one"?

The square of less than one refers to the mathematical operation of multiplying a number by itself. In this case, the number is less than one, meaning it is a fraction or a decimal.

What is the result of squaring a number less than one?

The result of squaring a number less than one is always a number that is smaller than the original number. For example, if you square 0.5, the result is 0.25.

Is the square of a number less than one always a positive number?

Yes, the square of a number less than one is always a positive number. This is because when you multiply a negative number by itself, the result is positive. Therefore, even if the original number is negative, the square will always be positive.

Can the square of a number less than one be greater than the original number?

No, the square of a number less than one can never be greater than the original number. This is because when you square a number less than one, the result is always smaller than the original number.

How is squaring a number less than one useful in science?

Squaring a number less than one is useful in science for calculating areas and volumes of objects that have dimensions less than one. It is also used in statistical analysis, such as calculating variance and standard deviation.

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