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Re: [OM] Your Basic FStop

Subject: Re: [OM] Your Basic FStop
From: Christopher Biggs <chris@xxxxxxxxxxxxxx>
Date: 28 May 1998 16:17:11 +1000
John Austin <j_austin@xxxxxxxxxxx> moved upon the face of the 'Net and spake 
thusly:

> Winsor,
> 
> I'm sure you know the basic scale, f1, f1.4, f2, f2.8, f4, f5.6, f8, f11,
> f16, f22, f32, f45, f64, f90. To determine the difference between odd f
> numbers simply subtract the smaller number from the larger number between
> two adjacent f stop values. The difference determines the number of steps
> between the two. Now simply calculate the percentage the odd number is of
> the total steps and you have it. For instance, f1.7 . Subtract 1.4 from 2
> and you get six steps. F1.7 is three steps away from both 1.4 and 2. That
> means f1.7 gives one half stop less light than f2 and one half stop more
> light than f1.4 . f1.8 would calculate out to two thirds stop more than f1.4
> than and one third stop less than f2. The difference between f4 and f5.6 is
> sixteen steps, so f5 is ten steps greater than f4 or approximately two
> thirds of a stop greater, and one third stop less than f5.6 . Works for all
> the f stop values. Just a quick math problem in your head. By the way,
> Olympus is not the only manufacturer to assign odd f stop values. Almost all
> of them do. Lets them advertise a faster lens.
> 

Linear interpolation is a good approximation for small differences,
but since the progression is _geometric_[1], not linear, the
exact difference in stops between two f-numbers F1 and F2 [1]can be
given by

          log ( f1 / f2 ) 
          ---------------
          log ( sqrt(2) )

(where f1 is the larger of the two numbers).

So for example f/1.8 is 0.304 of a stop wider than f/2
               f/1.2 is 0.445 of a stop wider than f/1.4
               f/1.8 is 0.725 of a stop more than f/1.4

Enjoy,
        Chris.
        

[1] Each f-number is the previous number multiplied by the square root
        of two.   Approx 1.414214
[2] Where F1 is the larger of the two numbers


--
Christopher Biggs -- chris@xxxxxxxxxxxxxx - Ph+61-7-3270-4266 - PGP & MIME OK
There's a bug in my mailer that mangles my sig but V guvax V'ir svkrq vg abj.
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