[Leica] 1.8 vs. 1.4!?!?

[filippiniaia at hotmail.com (Matthew B. Filippini)]

Time to beat a dead horse!  If anyone is interested:
 
It is all geometry, namely the area of a circle.
 
For each f-stop, we have double the light.  The f-stop is related to the 
size of the aperture, which is approximated as a circle.  The amount of 
light coming is proportional to the circle?s area, which you may recall is 
pi times the radius squared, pi*r^2.  We use the f# for the equivalent 
radius.
 
Thus, starting with f1, and r = 1, the area is pi*r^2 = pi*1*1 = pi, as the 
relative amount of light.
 
For an amount of light 2*pi (next f-stop, double the light), pi*r^2 = 2 pi.  
Divide both sides by pi, and you get r^2 =2.  r = the square root of 2, or 
1.414?  f1.4 is the next stop.
 
This is where the 1.4 factor George mentioned comes from; the square root of 
2 is 1.414.
 
Next f-stop, double the light again: pi*r^2 = 2*2 pi. r^2  = 4, f2 is the 
next stop.
 
So, if you want fractional stops:
 
1/3 stop:   Square root of 1.333 = 1.15456
1/2 stop:   Square root of 1.5     = 1.22474     
2/3 stop:   Square root of 1.667 = 1.29112
 
So going back to Mark?s f1.4 example:
1/3 stop slower = 1.414 * 1.15456 = f1.633 or f1.6
1/2 stop slower = 1.414 * 1.22474 = f1.732 or f 1.7
2/3 stop slower = 1.414 * 1.29112 = f1.828 or f1.8
1 stop slower = 1.414 * 1.414 =  f2.0

 
Matt
 
 





On Nov 2, 2011, at 5:32 PM, Mark Rabiner wrote:

> I looked up f 1.8 vs. 1.4 thinking it was between a half and a quarter of a
> stop and they are saying its 2/3rds!?!?! Anybody know that that's true?
> 
> Where is there a photo calculator that tells you these things?!?!?

I always thought the basic math for 1 f stop revolved around a factor of 1.4.
1.4 x 1.4 = 1.96
1.8 / 1.4 = 1.29

so - yes - 2/3 would seem close enough for?
what? I'm not sure.

Regards,
George Lottermoser 
george at imagist.com
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