Understanding the Inverse Square Law for Laser/Coherent Light

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Discussion Overview

The discussion revolves around the application of the inverse square law to laser or coherent light, exploring how laser beams behave over different distances and the factors influencing their divergence. The scope includes theoretical considerations, technical explanations, and some mathematical reasoning.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that the inverse square law applies to laser light at long distances but not at short distances due to the coherence of the beam.
  • Others contend that laser beams begin to diverge immediately upon leaving the output mirror, although this divergence is minimal at short distances.
  • One participant notes that measuring the intensity of a laser signal under the assumption of a point source would yield incorrect results due to the beam's properties, which do not conform to the r-2 law.
  • Another participant suggests that all light sources, including lasers, emit light into a non-zero solid angle, making the inverse square law relevant in some capacity.
  • There is a discussion about determining the radius of a laser beam based on its starting radius and divergence angle, indicating the need for specific parameters to make such calculations.
  • One participant expresses confidence that the problem can be solved analytically or through direct proportion, while another simplifies the concept to basic geometry.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the inverse square law to laser light, with no consensus reached on the conditions under which it applies. The discussion remains unresolved regarding the relationship between laser divergence and the r-2 law.

Contextual Notes

Limitations include assumptions about the divergence angle and the nature of laser light emission, which are not fully explored or defined in the discussion.

Glenn
Does the inverse square law apply to laser/coherent light?
 
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No at short distances, yes at long distances. The coherence keeps it from spreading, however, because the aperture is finite, it eventually starts spreading.
 
It is not a matter of starting to spread. The laser beam begins diverging as soon as it leaves the output mirror. The divergence is very small, so for small distances the net divergence is essentially zero. If you measure the spot size at various distances the divergence is noticeable. It is especially noticeable over any distance out side of a lab. So the spot size from a Earth based laser on the moon is appreciable. Beam divergence is not governed by r-2 laws, it is a result of properties of the laser itself.

Now, if someone were to measure the intensity of the laser signal on the moon, and assumed that it was the result of a point source radiating equally in all directions (i.e. they applied r-2 law they would arrive at an astronomically large number for the energy of the source. One of the big advantages of a laser is the ability to put a significant amount of energy into a very narrow beam.

I believe that r-2 laws only apply to sources which emit energy into a significant portion of a sphere.
 
Originally posted by Integral
I believe that r-2 laws only apply to sources which emit energy into a significant portion of a sphere.

Then how can we determine the radius of a laser beam with a given distance and starting radius?
 
Originally posted by kishtik
Then how can we determine the radius of a laser beam with a given distance and starting radius?
You have to also be given the divergence angle.

And Integral, any source emits light into some non-zero solid angle -- lasers included -- and so 1/r2 is always relevant.

- Warren
 
Originally posted by chroot
You have to also be given the divergence angle.
I had no idea about that but now I think that shouldn't be hard with the div. angle. We can solve it analitically or using direct proportion. Am I wrong?
 
It's just middle-school geometry.

- Warren
 

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