On Tue, 24 May 2005, Don Sanderson wrote:
How does one figure partial stop numbers?
For instance what stop is half way between 4 and 5.6?
And where does 4.76 fall? This is a 2.8 lens with the
SMCP-F 1.7x converter.
I'm guessing there is a simple multiplier for this but
with my limited knowledge of math I have no clue
what it is.
This is more out of curiosity than necessity.
Someone posted a link to this info but I can't find
it again.
TIA
Don
IIRC, f-stops are defined by the *diameter* of the aperture, but
light transmission goes as the *area* of the aperture. Thus, doubling the
diamter (i.e. f/8->f/16) *quadruples* the light transmission. A "stop" is
defined as a doubling/halving of the light, so f-stops at a ratio of
sqrt(2) \approx 1.4 are one "stop" apart.
Fratio = (sqrt(2))^N where N is the number of stops. Solving for N
yields:
N = (2 log(Fratio))/(log(2))
e.g.... your question:
(2 log(4.76/4))/(log(2)) = 0.5, or 1/2 stop
The 1/2 stop ratio is 2^(1/4) = 1.189 \approx 1.2
The 1/3 stop ratio is 2^(1/6) = 1.122
So these sizes are "1/2 stop" apart:
1.4 -> 1.7 -> 2 -> 2.4 -> 2.8 -> 3.4 -> 4 ...
and these are "1/3 stop" apart:
1.4 -> 1.6 -> 1.8 -> 2 -> 2.2 -> 2.5 -> 2.8 ...
-Cory
*************************************************************************
* Cory Papenfuss *
* Electrical Engineering candidate Ph.D. graduate student *
* Virginia Polytechnic Institute and State University *
*************************************************************************
