IronGoober
Interfector Viris Spurii
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...and now, No. 1, the larch...
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If you look up the resolving power of the human eye, it is about 20 arcsec (from the diffraction limit and the size of the aperture of the human eye, i.e. pupil.) but it is less in actuality due to eye aberrations. But if we assume 20 arcsec, that's about 2.8e-4° or 9.7e-5 radians. Using the approximation sin(theta)=theta (i.e. object radius/distance = theta), you can calculate the size of the object that one should be able to see.
So for a 1" coin, --> r=1.27cm, solve for distance, ~13092cm, or 130m. That is a best case scenario if you had absolutely perfect eyes. It will be much less than that in practice, depending on your eyes, likely 1/2 or a 1/3 of that.
For something that is shiny and that diffusely reflects light, you will be able to make it out just from the reflection, but you won't actually be able to resolve it (i.e make out the shape). You'll only be limited in distance by how low of light intensity you can detect (as the light intensity will fall off 1/r^2). I think that is what you were detecting was the diffusely scattered light from the coin.
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