NavList:

Jared you wrote:

"Two minutes of angle ("MOA") at 100
yards would be "typical" but that's a limit of the rifle not the shooter.
1/2 MOA is not unusual in competitions, that is, five rounds in a 1/2"
radius. But that's not so much from the human eye, but from extreme skill at
holding the weapon steady, and preparing the rifle and ammunition to extreme
tolerances, then either judging the wind very well or shooting on a calm
day"

 

I can see what you mean, but consider this: If visual resolution issues were irrelevant, you would get those five rounds in a tight cluster from a steady hand, but they would not necessarily cluster at the center of the target. The eye has to enter into it. I liked Alex's thought that the circle around the center is the primary visual clue and that could permit sub-arcminute accuracy in aiming.

 

And:

"You'll find resolution limits of the human eye somewhere out there on the
web. They vary somewhat as does vision, i.e. farsighted? 20-20? 20-20 is
supposedly normal, but 20-10 and even 20-5 exist. Even without genetics,
there's a lot of variation in eyes."

 

I did as you suggested and went looking on the web. I googled on "angular resolution human eye". There's a lot of variety. More than one astronomy site mentions something in the range of 3 to 10 minutes. This is clearly not correct and, as I mentioned in another message, I think it's influenced by the Mizar and Alcor story. A number of sites calculate the formal diffraction limit resolution from theta=3438*1.22*lambda/D [theta is the limiting angle in minutes of arc, lambda is the wavelength of the light being observed, D is the diameter of the aperature, and 3438 converts the angle to minutes while 1.22 results from the specifics of a circular aperture]. This calculation is important but I think it misses the point that the eye is an optical system sitting on top of a detector array --it's the retina that sets the real limit. You can't do *better* than the diffraction limit, but that doesn't mean that this is the actual resolution of the eye. And finally there are a number of sites that talk about empirical tests and most of these say "about 1 minute of arc".

 

Of course my optics laboratory is close at hand (my optics lab is my kitchen...), so I decided to do some simple testing with my own pair of detector arrays. I drew various shapes on an index card taped on a wall: pairs of dots, pairs of thick black lines, pairs of thin red lines, pairs of blue dots, etc. Then I moved away from the card until I couldn't see the difference between the pairs anymore. The specific geometry and colors made some difference (lines are easier to split than dots) but in every case I got a resolution of 1.2 to 1.7 minutes of arc. Next I did similar patterns cut into a piece of aluminum foil taped over a flashlight and turned out all the lights. The results were in the same range.