# L-Numbers: an Alternative to F-Numbers

One thing I regularly see in newcomers to photography, is the confusion created when first met with the Exposure Triangle.

For those unfamiliar with the Exposure Triangle (or just its name)…

The Exposure Triangle is the system whereby a photographic exposure can be adjusted, by changing any two of three parameters (shutter speed, aperture and sensitivity), in equal and opposite amounts, without affecting the overall image lightness.

For example: you can halve the shutter speed if you double the sensitivity. And so on.

“That’s not difficult,” I hear you say—and I would agree. A sensitivity of ISO 400 is double that of ISO 200; a shutter speed of 1/60 second is half that of 1/30 second—it’s not rocket science. Wait, what about Aperture? An aperture of f/2.8 is double that of f/4?! Say what?

To better understand what the hell is going on with F-Numbers, you need to understand optics. But, you don’t want to be doing that at the same time as you’re trying to explain the Exposure Triangle (or anything else, if we’re honest). It’s complicated enough for the newcomer. Even for seasoned photographers, the current aperture scale sometimes causes a short pause or scratch of the head. Sensitivity and Shutter Speed are both self-explanatory and intuitive, so why not Aperture?

I started to ponder this question when I was writing my article explaining Aperture’s f-number system in 2009. It seems that photographers and camera makers are settled on the current “f/5.6” jargon, and have been for a very long time. I suppose every discipline has its own varying amounts of jargon, so why not photography? Accessibility, I suppose, would be the answer.

### Doubling the power should double its written value

So, I set about coming up with an alternative. Being a maths geek in my youth, and understanding the Inverse-Square Law (which applies to projected images), it seemed obvious to me that this was the way to go. Aperture is a measure of light-gathering power, and it should look like it. Doubling the power should double its written value.

The current Aperture notation system doesn’t take aperture area into account—only diameter. That’s madness. Effectively, this means that the relationship between aperture and its notation is non-linear. So, let’s scrap that for a start.

Light intensity is proportional to the square of the diameter (aperture area), and inversely proportional to the square of focal length (image spread). A quick calculation on the back of an envelope shows that light-gathering power is inversely proportional to the F-number squared. We’re getting nearer, but the figure still goes down when it should be going up 1.

This is where the leap of faith comes in. The inverse of the squared F-number is a tiny fraction, and nobody likes fractions. So, let’s multiply the whole thing by a magic number—I propose 1024. Why 1024? Because it is 210 (2x2x2x2x2x2x2x2x2x2), or about 1000, making sense to both humans and optics nerds.

### Whoah! Hold on a minute. What did you just do there?!

Bear with me. I think this is better-explained by example. Let’s take a few common Aperture settings…

F-number  Square  Invert 1  x 210  (x approx 1000)
1.4  2  1/2  512  (500)
2  4  1/4  256  (250)
2.8  8  1/8  128  (125)
4  16  1/16  64  (60)
5.6  32  1/32  32  (30)
8  64  1/64  16  (15)
11  128  1/128  8  (8)
16  256  1/256  4  (4)

Now, do you see what I did? An f/1.2 lens would have a light gathering power of 700. Ansel Adams’ (allegedly) favourite aperture of f/64 would have had a light gathering power of 0.25. Now you can really see the difference.

You may have come up with an excuse for dismissing this idea: it’s too complicated. But, really, it’s not. Rather than remembering a strange set of numbers, you just need to remember a logical set of numbers. Like with decimalisation: you’re not supposed to convert, you’re supposed to adjust.

So the final ingredient in this proposal has to be a new name. We can’t call it Light Gathering Power—it’s a bit of a mouthful. How about just plain old “L-Number”, as in L60, or L500? So, you might take a photo with settings of: L64 at 1/125s & ISO100. Need more depth of field? How about L32 at 1/60s & ISO100, or L32 at 1/125 & ISO 200. You know it makes sense.

An interesting side-effect of this system is that the proposed L-Numbers are also proportional to lens price.

Discuss…

1. Although, technically/pedantically, the F-number is actually already inverted, which is why it should be written with a fraction bar, like f/8, meaning: f divided by 8.

Keith Nuttall, 2014

## 3 thoughts on “L-Numbers: an Alternative to F-Numbers”

1. EricY

Great idea. This would remove a big stumbling block for newcomers to photography. Even for a tech savvy person, the way a smaller number lets in more light and being locked to a scale with fractional numbers simply aren’t intuitive, considering the only intent is to specify the size of a hole.

2. Roy Nash

Ansel Adams did indeed favour f64 which has a very small light gathering power. He was a member of a group of photographers who called themselves Group f64. Imogen Cunningham and Edward Weston were also members. Their quest was for the maximum possible depth of field. At f64 virtually everything was in focus from about 2 metres to infinity with the lenses they used. Some of their cameras had lenses with apertures of f128 ! You might be wondering why modern DSLRs don’t have f64 or f128. This is for two reasons. (1) A matter of scale. The lenses Ansel Adams used were much bigger than a lens for a 35mm camera so each aperture was physically much larger. Manufacturers found that making an f64 lens for a 35mm camera was impossible. (2) Even if it were possible and maybe now it would be, having the very tiny hole required would cause problems due to diffraction. Even at f32 this can be a serious problem. This is one of the advantages of working with large format cameras like Ansel Adams. You can stop them down way below f32 without losing any detail.