Archived posting to the Leica Users Group, 2008/12/13

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Subject: [Leica] Re: Summaron: a very long post about a small lens.
From: glehrer at san.rr.com (Jerry Lehrer)
Date: Sat Dec 13 16:18:28 2008
References: <200812130331.mBD3VQoT089665@server1.waverley.reid.org> <A3B2C7B3-4107-4F30-A014-39B9943526A6@optonline.net> <20081213175209.7C8AB71177@barracuda.rutabaga.org> <3B025B86-25C5-4DF6-8656-C7144604BB5C@bex.net>

Howard,

Figures can't lie, but----------etc!

Jerry


Howard Ritter wrote:
> 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
>
>


In reply to: Message from lrzeitlin at optonline.net (Lawrence Zeitlin) ([Leica] Re: Summaron: a very long post about a small lens.)
Message from marcsmall at comcast.net (Marc James Small) ([Leica] Re: Summaron: a very long post about a small lens.)
Message from hlritter at bex.net (Howard Ritter) ([Leica] Re: Summaron: a very long post about a small lens.)