just don't seem right...

A

allegansveritatem

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Jan 10, 2018
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Here is problem:visualprob.PNG
Here is how I worked out part a)
visuala.PNG

and b)
visualb.PNG

I don't know about anyone else, but I know for a fact that I can't see a 6 inch pen that is held a thousand feet away, and I really don't think anyone else can either so ...where have I gone astray? I've gone over this several times but keep coming back to these results.
 
I initially thought I saw two mistakes in your work, but on going through it carefully it looks like you did fine.

It may be time to check your vision ...

EDIT: Or we can check whether their claim is right. According to Wikipedia, human vision can resolve at best 0.008 degrees; and "normal" vision can resolve one minute of arc. In radians, that is [MATH]\frac{1}{60}\times\frac{\pi}{180} = 0.00029 radians[/MATH]. That's actually about half of what they claim, so maybe they are right. Send a friend 1000 feet down the road holding a 6 inch pen (or, better, a piece of paper with a 6-inch diameter circle on it), and see what you can see ...
 
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You are not asked to recognize a pen at 1000 feet. You are asked whether you see 2 points 6" apart as one point. This might be possible.
 
I'd wonder if you can see the person holding the paper 1000 ft away.
 
Dr.Peterson said:
I initially thought I saw two mistakes in your work, but on going through it carefully it looks like you did fine.

It may be time to check your vision ...

EDIT: Or we can check whether their claim is right. According to Wikipedia, human vision can resolve at best 0.008 degrees; and "normal" vision can resolve one minute of arc. In radians, that is [MATH]\frac{1}{60}\times\frac{\pi}{180} = 0.00029 radians[/MATH]. That's actually about half of what they claim, so maybe they are right. Send a friend 1000 feet down the road holding a 6 inch pen (or, better, a piece of paper with a 6-inch diameter circle on it), and see what you can see ...
Click to expand...
well, I have been decidedly myopic my entire life (alas, in more ways than one) and so the thought of seeing a pen at 333..333 yards is ,to say it plain, unthinkable for me. But...it must be so, In read it in a book!
 
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One thing that makes me question the question is that the width of the pen will be less (much less) than 6 inches, so even if you can distinguish the ends of the pen, you can't distinguish its sides. That is, it may well be too thin to see, even if it's long enough. It may slip between the "pixels" of your eye. (This is why I suggested changing it to a high-contrast circle rather than a pen.)

The reference I gave specifically points out that acuity is best in daylight, using cone cells. But I suspect if each end of the pen held a point source of light it might fit the description of acuity.
 
Jomo said:
I'd wonder if you can see the person holding the paper 1000 ft away.
Click to expand...
That surprised me, Jomo, so I just walked to the end of the driveway (to see what I could see), and I easily saw kids in the street five blocks away. I drove down there; the odometer indicated a quarter mile (i.e., more than 1300 feet).

?
 
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