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According to this diagram:

Inverse square law

And a few articles I have read, the number of photons emitted from a point source is exactly the same, and the reason why we detect fewer photons as we move away from the source is because the photons spread over distance. If that's true, then why is there specific distance that light can travel in a medium like tap water (2 m) or distilled water (8 m) or ice beneath the south pole (about 100m - 200m)? Is it because photons are absorbed by that medium? And if I were to have a point source in "total" vacuum which emitted about 10,000 photons. If I went away from that source by 1 kilometer or two and surrounded the entire source by a sphere, will I detect all of those 10,000 photons?

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As you suggest the fall in intensity with distance in water, ice, etc is because the photons are absorbed. If you did your proposed experiment in space you would indeed detect all 10,000 photons.

There is a minor complication that we need to be aware of. If you shine a beam of light through some material then the light can be scattered as well as absorbed. So for example clouds are white not because they absorb the light but because the water droplets in the cloud reflect the light sideways and scatter it. If the water/ice/whatever just scattered the light then you would still detect all 10,000 photons but their original directions would have changed.

However water does absorb photons as well as scatter them. Water doesn't absorb light strongly, which is why the path length is quite long. However any dielectric, even apparently clear ones like water, will absorb light to some extent due to the interaction between the electric field of the light and the electrons in the dielectric.

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  • $\begingroup$ Okay, thanks. And because of the inverse square law, is it possible for me to detect light from any arbitrary distance (assuming it does not get absorbed or reflected in its path) if I move around a little (assuming that I am capable of detecting a single photon)? So, if I am about 10 m away from a point source and I detect about 10 photons. If I move 100 m away, I should detect one photon, BUT if I move around, I should still be able to detect 10 photons, right? $\endgroup$
    – Always Learning Forever
    Commented Aug 27, 2017 at 5:42
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    $\begingroup$ @AlwaysLearningForever: see my answer to Photons from stars--how do they fill in such large angular distances? The photons are delocalised so you can always detect them. $\endgroup$
    – John Rennie
    Commented Aug 27, 2017 at 5:54

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