Another approach yet (using the same formulas, BTW)
When you take the basic f-stop range 1, 1.4, 2, 2.8, etc.
the f-numbers, starting from 1 (the Base!), are each sqrt(2) times
their predecessor. Or: each is 2 to the power 1/2 times its
predecessor (=1.141213562)
If you want the division to be twice as fine, you will have to
make each number 2 to the power 1/4 times its predecessor
(=1.189207115)
and if you want to cut the distances between the original f-numbers in
three, you must make each one 2 to the power 1/6 times its predecessor
1/6
For example in the last case: ( 2 ) = 1.122462048
The range develops like:
1.000 1
1.122
1.260
1.414 1.4
1.587
1.781
2.000 2
2.245
2.520
2.828 2.8
3.175
3.564
4.000 4
4.490
5.040
5.657 5.6
6.350
7.127
8.000 8
8.980
10.08
11.31 11
12.70
14.25
16.00 16
etcetera (not the computer which made this table, but me typing them
over gets fatigued now...)
As you also can see from the table, there is hardly any rounding off
error in all 'normally' used f-numbers....
Thanks to math,
Frank van Lindert
Utrecht NL
On 28 May 1998 16:17:11 +1000, Christopher Biggs
<chris@xxxxxxxxxxxxxx> wrote:
>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
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