Re: distant wires

[T3D john bercovitz <bercov@xxxxxxxxxxx>]

BobH writes:
 
> I also think that there is more "than meets the eye". A good 
> example is a distant telephone line against the sky. Its small 
> diameter at that distance subtends an angle far below the 
> resolving power perhaps but we see it because a long row of 
> rod/cones are affected and somehow recognize it. Perhaps part 
> of our pattern and edge acuity in the brain?
 
I have a very old friend with very fine eyes who saw an 8" cable 
at 10 miles against a bright sky many many years ago.  This is 2 
or 3 seconds of arc.  But it was a single cable widely separated 
from its mates.  I wouldn't say he had resolved the cable.  I 
would say he had seen the peak of the diffraction pattern of a 
high contrast line object on the retina of his eye.
 
Consider that the receptors in the eyes are a couple of microns on 
center at closest.  That comes out to about half a minute of arc 
of  resolution.  Also consider that the resolution of the eye 
peaks (because of a balance of aberrations and diffraction and 
other factors) at a pupil diameter of 3 mm.  Remembering the 
Rayleigh criterion and the simple rule which ensues that the 
angular resolution of an optical system such as this is 
 
(115 second of arc - mm)/(diameter of the entrance pupil in mm)
 
you find that the resolution of the eyes is 115/3 which is again 
about half a minute of arc.  This is in a perfect eye under the 
best of conditions (high contrast object).  If the eye has any 
problems at all, there is a reduction in its resolution which 
leads us to the ordinary eye's resolution of 1 minute of arc.
 
If you're a fine mathematician, which I certainly am not, you'll 
have no trouble applying your transforms and Bessel functions to 
find the diffraction pattern laid on the retina by the high 
contrast line object and the round entrance pupil.  I'm sure 
you'll find its central peak is more than dark enough to stimulate 
the receptors of the eye.
 
John B


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