f-stop increments on scale?

[dh003i]

On most my lenses, between major f-stops, here are 2 demarkations, like so:

f/11
-
-
f/16
-
-
f/22
-
-
f/32

Each of the larger f-stops is 1 stop faster -- 2x as much exposure for a given time -- than the preceding one. So are the increments 1.33x and 1.67x faster than the larger numbered stop?

I.e., does that correspond to:

f/11
- f/13.1
- f/14.6
f/16
- f/18.5
- f/20.7
f/22
- f/26.1
- f/29.18
f/32

[Robert Hughes]

f/29.18 ? Um, sure, but ... does that look much different from f/29.23 ?

[BradS]

Well not exactly....the relationship is as follows:

f = 2 ^ (Av/2)

where f is the f stop number and Av is the aperture value. The Av is linear the f stops are not.

so....it is really:

Av---------- f
6 ---------- 8.00000
6-1/3 ----- 8.9797
6-2/3 ----- 10.079
7 ---------- 11.314
7-1/3 ----- 12.7
7-2/3 ----- 14.254
8 ---------- 16
8-1/3 ----- 17.959
8-2/3 ----- 20.158
9 ---------- 22.627
9-1/3------ 25.398
9-2/3 ----- 28.509
10 -------- 32

[dh003i]

BradS,

Thanks, got it. So to go the other way, from f-stop to Aperture value, it's Av = 2 lg(f), where lg is base-2 log.

I see how Aperture value relates to talk of +/- 1/3, 2/3, or 1 stop...but I've never seen it really used anywhere else. I use a DSLR for metering with my 4x5. Is there a need to use aperture-value for anything?

[BradS]

Hmmm, it is kinda complex....in a nutshell,

The Aperture value is just one piece of the total exposure equation in the Additive Photographic Exposure (APEX) System. It used to be used quite frequently before electronic light meters became widely available...and it is what the light meter does internally....in a nut shell...

S + L = A + T

Where:

S is the film Speed value
L is the Light Value
A is the Aperture value and,
T is the Time value (related to the shutter open time).

Doug Kerr explains it all very well in a document on his web site. See this PDF at Doug's Web Site.

As we have seen (above) the Aperture value (Av) is related to the f stops. In a similar manner, there is a relationship between Time values, Tv and shutter speeds. And likewise between film speeds and Speed values.

Photography books used to explain all this stuff before light meters made it arcane.

[BradS]

So to go the other way, from f-stop to Aperture value, it's Av = 2 lg(f), where lg is base-2 log.

yes. That is correct....or, equivalently,

2 * log(f) / log(2) = Av

where log is the natural log (or common log - it doesn't matter).

by definition, log base 2 of X is exactly log of X divided by log of 2.

[Bob Salomon]

Photography books used to explain all this stuff before light meters made it arcane.

Not really, Hasselblad 500 lenses and Rolleiflex E and F models had a cross coupled aperture and shutter speed control. You set the EV (exposure value) number on the camera or lens and then when you changed either shutter speed or the aperture both changed at the same time to maintain the same exposure value at the new shutter speed or aperture setting. This control was easily disconnected if you did not want to maintain the constant EV value. And those Rolleis had built-in coupled exposure meters and Hasselblad sold one that was in the accessory finders or one that replaced the winding knob. So these were features on cameras made well after exposure meters came on the scene. Other cameras like the Retina, the Contaflex, the Bessamatic, etc. also had this feature. Note, these are all leaf shutter cameras, not focal plane shutter cameras.

[Bob Salomon]

As for the stops between full stops on a shutter. It is an interesting exercise to try to memorize what the actual values may be but from a picture taking standpoint it is a wasted exercise. The intermediate stops are in 1/3rd, 1/2 or 1/10th stop increments, depending on the shutter. You are either increasing or decreasing the exposure by one of those values when you set the aperture at one of them. Knowing it is 29.18 is immaterial. Photographically it is f22 and 2/3rds. You will have a very difficult time finding a reference as to what those stops actually are.

[r_a_feldman]

My Weston Master Model 715 exposure meter has the following f: numbers on its dial:

1.5, 1.8, 2, 2.2, 2.5, 2.8, 3.2, 3.5, 4, 4.5, 5, 5.6, 6.3, 7, 8, 9, 10, 11, 12.7, 14, 16, 18, 20, 22, 25, 29, and 32.

The numbers from 8-32 are the same as BradS posted, rounded to whole numbers, except for 12.7 for some reason.

[BradS]

My Weston Master Model 715 exposure meter has the following f: numbers on its dial:

1.5, 1.8, 2, 2.2, 2.5, 2.8, 3.2, 3.5, 4, 4.5, 5, 5.6, 6.3, 7, 8, 9, 10, 11, 12.7, 14, 16, 18, 20, 22, 25, 29, and 32.

Interesting! Looks like they explicitly engraved the f numbers in 1/3 stop increments. Any idea when that model was made?