quiz: if you increase by 1/3 stop, how many % of total exposure are you increasing?

[jbq]

Moiz: these guys all agree that f-stops are logarithmic: http://www.wikipedia.org/wiki/F-stop http://members.rogers.com/davesphoto/id12.htm http://www.eyeconvideo.com/glossary_of_terms.htm http://www.cliffshade.com/dpfwiw/exposure.htm

 

Logarithms (by definition) are such that log(a*b)=log(a)+log(b), where the star & denotes a multiplication. They are also such that any two different number have different logarithms (this is enough of a definition to go and prove all the other properties of logarithms).

 

From here on, we know that log(2)=1 (an increase of one stop multiplies the exposure by 2). Let R be the multiplying factor that matches one third of a stop (mathematicians please don't chuckle). log®=1/3, meaning that log®+log®+log®=1, i.e. log(R*R*R)=1 (by definition of logarithms), i.e. R*R*R=2. R is the cubic root of 2.

 

Yes, I've cut a few corners, and I've taken the definition of logarithms that was most convenient for this "proof". Explaining with more details would take just too long and would bo so totally off-topic that it's not worth my time.

[travis1]

Im actually very afraid everytime a new message appears on this thread. Thx for the memories guys. ;)))

 

Im planning the next quiz.

[andy_piper2]

Maybe y'all should look at it from a different angle, to avoid the weirdness of square roots and aperture radius vs. area, etc.

 

Take a nice exact M7 electronic SHUTTER. Assume it lets through 1000 units of light in 1/500 second and 500 units of light in 1/1000 second (in the middle of the frame - no quibbles, PLEEZE!)

 

So, what shutter speed would give 1/3 more exposure than 1/1000 sec.? Or 2/3 more? Is 1/750 sec. actually giving the exact equivalent of 1/2 stop more exposure? Or should it be 1/707 second?

 

If we can get values for those shutter speeds (which should be easier), then we can come back to apertures-f/stops.

 

MY math sez the 1/3rd-stop shutter speeds should be 1/794 and 1/630, which follow the 1.26x rule. And that the correct 1/2-stop speed is 1/707 (and you always thought those readouts of 1/700 were just roundoff error from 1/750!).

 

1000:707 :: 707:500

 

- and -

 

1000:794 :: 794:630 :: 630:500

 

(I hope the spacing held up in those equivalences.)

[moiz]

Jean-Baptiste, thanks.