A question for you math wizards

First topic message reminder :

I hope the following makes sense.
 
I use blank wall dry fire, target dry fire and eyes closed dry fire as part of my training routine.  I would like to create a dry fire target whose black looks the same diameter at 12 feet as the black on a B-6 target looks at 50 yd.
 
As we know, the B-6 50 yd slow fire target has the 8, 9, 10 and X rings black with the 8 ring having a diameter of 8".  And when we are standing on the firing line looking at this target on the 50 yd line, the black looks small indeed.  What diameter black ring would give me the same perceived diameter at 12 feet?
 
Why 12 feet?  That is the distance from my always-keep-a-gun-pointed-in-a-safe-direction wall to a fixed table.  What wall is that?  It is the wall in my basement that if heavy forbid the gun actually goes bang, the bullet will go through the dry wall, into concrete block and if it gets through the concrete block, into soil.
 
Thank you.

p.s. A formula where you enter the distance and it tells you the diameter would be really great.

Frank, I stand corrected. I did drop some 3s. I would mention that neither one of us is actually correct. To get it perfect we need a measurement of the lens in the eye of the shooter at a known amount of light. That could make several .00001 of an inch difference.

Wobbly, What do you mean next thing? I already checked and found your calculation off by .0000000000000000000000000000000001 as you forgot to include the diffraction created by normal humidity of sun light! I didn't want to include that so as to make you look bad

I don't know what indecorous is trying to prove, I was always told that range scaling of targets was to compensate for bullet trajectory. Back when everyone was shooting iron sights and issued ammo using a 6 o'clock hold there would not be a need to adjust sights for range distance. I'm also told that the 50' target was made so as to add difficulty to avoid ties. He is using bullet diameter added to the ring diameter to determine MOA. I'm not sure what he's trying to prove yet he implies that the ring diameters benefit the better shooters.
 Maybe if I have time some day I can determine why the ring diameters are not consecutively reduced similar to international targets but it sounds like a lot of work to me! Possibly someone in the NRA can simply answer that question.
 Getting back to what the OP wanted to know as what the diameter of a 8" eight ring will look like if it were scaled back to 12' then it's simply .64"

Ok, for those of you who dislike math, here's a computer-generated (!) table of the scales of the black bull for all the NRA targets, out to 50 feet.  The distance between you and your target is on the left, followed by one column for each type of target, with the scale of that target's black rings shown (in inches).  I rounded to 2 decimal places, because, well, if you need more precision than that for the purposes of putting a black circle on your basement wall for dry fire exercises, you've got issues that math and small computer programs cannot solve for you. 

At a given distance (in feet), here is the size of the black (in inches)

Your
Distance   B-6    B-8    B-16   B-4    B-5    B-2    B-3
--------   ----   ----   ----   ----   ----   ----   ----
    0      0.00   0.00   0.00   0.00   0.00   0.00   0.00
    1      0.05   0.07   0.07   0.06   0.06   0.06   0.06
    2      0.11   0.15   0.14   0.12   0.13   0.12   0.12
    3      0.16   0.22   0.21   0.19   0.19   0.18   0.18
    4      0.21   0.30   0.28   0.25   0.25   0.25   0.24
    5      0.27   0.37   0.35   0.31   0.31   0.31   0.31
    6      0.32   0.44   0.43   0.37   0.38   0.37   0.37
    7      0.37   0.52   0.50   0.44   0.44   0.43   0.43
    8      0.43   0.59   0.57   0.50   0.50   0.49   0.49
    9      0.48   0.66   0.64   0.56   0.56   0.55   0.55
   10      0.53   0.74   0.71   0.62   0.63   0.61   0.61
   11      0.59   0.81   0.78   0.68   0.69   0.68   0.67
   12      0.64   0.89   0.85   0.75   0.75   0.74   0.73
   13      0.69   0.96   0.92   0.81   0.81   0.80   0.80
   14      0.75   1.03   0.99   0.87   0.88   0.86   0.86
   15      0.80   1.11   1.06   0.93   0.94   0.92   0.92
   16      0.85   1.18   1.13   0.99   1.00   0.98   0.98
   17      0.91   1.26   1.21   1.06   1.07   1.04   1.04
   18      0.96   1.33   1.28   1.12   1.13   1.11   1.10
   19      1.01   1.40   1.35   1.18   1.19   1.17   1.16
   20      1.07   1.48   1.42   1.24   1.25   1.23   1.22
   21      1.12   1.55   1.49   1.31   1.32   1.29   1.29
   22      1.17   1.63   1.56   1.37   1.38   1.35   1.35
   23      1.23   1.70   1.63   1.43   1.44   1.41   1.41
   24      1.28   1.77   1.70   1.49   1.50   1.47   1.47
   25      1.33   1.85   1.77   1.55   1.57   1.53   1.53
   26      1.39   1.92   1.84   1.62   1.63   1.60   1.59
   27      1.44   1.99   1.92   1.68   1.69   1.66   1.65
   28      1.49   2.07   1.99   1.74   1.75   1.72   1.71
   29      1.55   2.14   2.06   1.80   1.82   1.78   1.77
   30      1.60   2.22   2.13   1.87   1.88   1.84   1.84
   31      1.65   2.29   2.20   1.93   1.94   1.90   1.90
   32      1.71   2.36   2.27   1.99   2.01   1.96   1.96
   33      1.76   2.44   2.34   2.05   2.07   2.03   2.02
   34      1.81   2.51   2.41   2.11   2.13   2.09   2.08
   35      1.87   2.59   2.48   2.18   2.19   2.15   2.14
   36      1.92   2.66   2.55   2.24   2.26   2.21   2.20
   37      1.97   2.73   2.62   2.30   2.32   2.27   2.26
   38      2.03   2.81   2.70   2.36   2.38   2.33   2.33
   39      2.08   2.88   2.77   2.42   2.44   2.39   2.39
   40      2.13   2.95   2.84   2.49   2.51   2.46   2.45
   41      2.19   3.03   2.91   2.55   2.57   2.52   2.51
   42      2.24   3.10   2.98   2.61   2.63   2.58   2.57
   43      2.29   3.18   3.05   2.67   2.69   2.64   2.63
   44      2.35   3.25   3.12   2.74   2.76   2.70   2.69
   45      2.40   3.32   3.19   2.80   2.82   2.76   2.75
   46      2.45   3.40   3.26   2.86   2.88   2.82   2.82
   47      2.51   3.47   3.33   2.92   2.95   2.89   2.88
   48      2.56   3.55   3.40   2.98   3.01   2.95   2.94
   49      2.61   3.62   3.48   3.05   3.07   3.01   3.00
   50      2.67   3.69   3.55   3.11   3.13   3.07   3.06

Oh, look... for a simulated B-6 target at 12 feet, the black bull should be scaled to 0.64 inches.

PM me if you want the goofy little Perl script that generated this table.  But keep in mind that I'm just another Perl hacker, so don't expect poetry.

Dave

There is obviously a lot of brain power here.  I think I should have asked 'How do we eliminate the deficit and defeat ISIS in the next 2 months'.

Lol

Thanks for all the input.  I have created my dry fire target (see attached photo).  Since photography is my second hobby, I used Photoshop to create the target.  The black was created using the Elliptical Marquee Tool set to a style of Fixed Size, a width of .64" and a height of .64".  The beige background tries to emulate the beige color of the B-6 and B-8 targets.
 
Multiracer, ignore the bullet hole.  My bad.

Ok Thomas, that's just frickin' funny!
{Coffee shooting out my nose...}
Glen