Archived posting to the Leica Users Group, 2000/03/07

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Subject: Re: [Leica] F-stops
From: Skip Williams <skipwilliams@pobox.com>
Date: Tue, 07 Mar 2000 10:20:58 -0500

One more log for the fire.  Here's a table with all the answers.  It lists 
in order the powers of two, f/stop rounded up, and inter-f/stop increment.

  Pwr of 2       Fstop   Increment
  0.00    1.0
  0.17    1.1    1/3
  0.25    1.2    1/2
  0.33    1.3    2/3
  0.50    1.4
  0.67    1.6    1/3
  0.75    1.7    1/2
  0.83    1.8    2/3
  1.00    2.0
  1.17    2.2    1/3
  1.25    2.4    1/2
  1.33    2.5    2/3
  1.50    2.8
  1.67    3.2    1/3
  1.75    3.4    1/2
  1.83    3.6    2/3
  2.00    4.0
  2.17    4.5    1/3
  2.25    4.8    1/2
  2.33    5.0    2/3
  2.50    5.7
  2.67    6.3    1/3
  2.75    6.7    1/2
  2.83    7.1    2/3
  3.00    8.0
  3.17    9.0    1/3
  3.25    9.5    1/2
  3.33    10.1   2/3
  3.50    11.3
  3.67    12.7   1/3
  3.75    13.5   1/2
  3.83    14.3   2/3
  4.00    16.0
  4.17    18.0   1/3
  4.25    19.0   1/2
  4.33    20.2   2/3
  4.50    22.6
  4.67    25.4   1/3
  4.75    26.9   1/2
  4.83    28.5   2/3
  5.00    32.0
  5.17    35.9   1/3
  5.25    38.1   1/2
  5.33    40.3   2/3
  5.50    45.3
  5.67    50.8   1/3
  5.75    53.8   1/2
  5.83    57.0   2/3
  6.00    64.0
  6.17    71.8   1/3
  6.25    76.1   1/2
  6.33    80.6   2/3
  6.50    90.5
  6.67    101.6  1/3
  6.75    107.6  1/2
  6.83    114.0  2/3
  7.00    128.0

Skip

At 3/7/00 10:12 AM  +0000, you wrote:
>Some maths!!!
>
>f stops are calculated using the surface area of the lens.
>which is related to the diameter (pi r square  as you might remember)
>
>This you can recognize looking at the f stops at the lens:
>
>1 -- 1.4 -- 2 -- 2.8 -- 4 -- etc.
>
>which equals
>
>2^0 -- 2^0.5 -- 2^1 -- 2^1.5 -- 2^2 -- etc. (2^0 means 2 raised to the power
>of 0)
>
>so ...
>
>2^0.5 which also can be noted as square root 2 actualy is 1.1415...
>Al the figures engraved on your lens are truncated. You can see this when
>looking at the more smaller apertures. It starts with each second figure
>multiplied by two but at the end it changes: f1.4 f2.8 f5.6 f11! f22 f45!
>f11 is 2^3.5= 11,3.
>Look at this: f5.6 is 2^2.5. However 2^2.5 equals 5,65685 which is rounded
>off as 5.7
>So f5.6 is actually closer to f5.7
>
>The question is, what f stop is 1.5?
>or ... 2 raised to which power equals 1.5?
>This is caluclated by 2 log 1.5 (sorry for the math) which equals 0.58496
>We can find this number somewhere between 0.5 and 1 thus between f14. and f2.
>... right.
>
>0.58496 is 0.08496 higher than 0.5 (fstop 1.4)
>The next stop is 0.5 further (2^0.5 -- 2^1, one fstop, remember?!)
>and 0.08496/0.5 = 0.16992.
>
>This means f1.5 is 0.16992 stop further than 1.4
>which equals 1/5.88512 or more or less 1/6
>
>so ...
>
>f 1.5 is +/- 1/6 smaller compared to f 1.4
>(possible truncation of 1.5 and inaccuracies of measuring the
>actual apperature not taken into account)
>
>
>Yet another answer!!!
>
>
>Richard.


- -----------------------------------------------
Skip Williams
Westfield, NJ
skipwilliams@pobox.com
http://www.skipwilliams.com
- -----------------------------------------------