[Leica] Half stop, third stop, stop the madness

[hlritter at bex.net (Howard Ritter)]

No, it actually is MORE than 1/2 stop, not less, and way more than 1/3  
stop. Remember, f/4 is already a full stop down from  f/2.8, so the  
jump from f/2.8 to f3.5, already well over halfway numerically, is way  
more geometrically.

Squaring the reciprocal of the f-ratio gives a number that is  
proportional to the aperture's area.
A full stop is an areal ratio of 2, corresponding to a ratio between f- 
ratios equal to the square root of 2. A half-stop is an areal ratio of  
sqrt (2), about 1.4, corresponding to a ratio between f-ratios equal  
to sqrt(sqrt( 2)), about 1.189.

2.8 x 1.189 = about 3.3.
3.3 x 1.189 = about 3.9.
So 1/2 stop down from f/2.8 is about f/3.3, with another equal- 
proportion areal step down to f4.

One-third of a stop is an areal ratio of the cube root of 2 (for three  
equal-proportion areal steps from one full stop to the next),  
corresponding to a ratio between f-ratios equal to the cube root of  
sqrt(2), or about 1.12.

2.8 x 1.12 = about 3.1.
3.1 x 1.12 = about 3.47.
3.47 x 1.12 = about 3.9.
So 1/3 of a stop down from 2.8 is about f/3.1, with two more equal- 
proportion areal steps down to f4.

So from f/2.8 to f3.5 is actually 2/3 stop. Unless you were talking  
about going from f/4 to f/3.5, which is 1/3 stop. (If you turn it  
around and take 4/1.12, you get 3.57. The numbers are rounded because  
they're irrational except for the alternate full stops f/1, 2, 4, 8,  
16..., as well as approximated in order to give numbers ending in an  
even digit or a 5.)

--howard


On Dec 13, 2008, at 12:50 PM, Marc James Small wrote:
> At 12:05 PM 12/13/2008, Lawrence Zeitlin wrote:
>
> >
> >I simply quoted Emil Keller's book. He was there. None of use were.
> >He specifically mentions the lens as an f3.5 Summaron although he
> >does err in stating that the diaphragm modification added a full stop
> >instead of half a stop.
>
>
> Larry
>
> With respect, it is a third of a stop, not a half-stop.  The  
> European apertures are 1/3 of a stop different from the  
> International scale which has been the norm since the 1950's.
>
> Marc