A Guide to Measurements in Photography – Part One

Tunnels of Time
Creative Commons License photo credit: fdecomite

“Let the scales fall from your eyes.”

If you’re new to photography, welcome to a world of crazy scales – where up is down, and less is more. There is of course a logic to the madness and rhyme that goes with every reason, but until it’s explained to you, it can seem rather hit and miss – and lots of miss. If you’re not too hot with your high-school arithmetic, some of this may feel too technical – but bear with it, and don’t be surprised if you can’t wrap your brain cells around the idea. Just bookmark this article and return next time you’re feeling bright and bushy-tailed.

OK; here goes:

(And don’t forget, there’s a big dictionary of photography on this site – the biggest on-line – so you can look up any words.)

f / number

This is probably the single most confusing measurement scale ever invented in the history of humankind. It seems to be everyone’s favorite – there are hundreds of web pages explaining it! Indeed, there’s already an article explaining aperture on our very own site.

A quick reminder of the main points: f/number is a measure of effective lens aperture compared to focal length, and is more or less synonymous with the terms f/stop or lens stop.

The reason we compare aperture to focal length – that’s what dividing does – is to make the f/number scale so that the same f/number results in the same exposure, irrespective of focal length. In the early days of photography, when lens coating was limited, there was significant light-loss which made f/numbers a little inaccurate (in cinematography they use still use T-numbers: see below) but in practice exposures are near enough the same in modern photography.

The reason we write it “f” with a forward slash is that it’s a number that invites a divisor – the number which divides into it. We are dividing the effective diameter of the aperture (strictly the effective diameter of the hole as seen from the front of the lens) into a constant number, the focal length. Now, if you divide into a fixed number with a big number, the result is smaller: that is why f/numbers like f/22 indicate a smaller aperture and less light coming through the lens, while a f/number like f/4 indicates a larger aperture with more light coming through. It is not correct to write “f-number” or “f-stop”.

You go to top of class if you’re wondering what happens with zoom lenses. Yes, as the focal length changes, so does the aperture for the same f/number. This is done either mechanically using a cam or roller in a slot to change the aperture as the zoom control is changed, or it’s done electronically, with the camera making adjustments when the lens tells it that you’ve zoomed i.e. changed the focal length.

And the reason I refer to “effective” diameter is that the majority of apertures are not circular, but pentagonal or hexagonal or some other weird shape. But it’s the area of the aperture that we’re interested in, so we look at a circular hole with an equivalent area and work from its diameter.

Anyway, another reminder: the scale starts at about f/1.4 as the largest commonly used aperture – a new Leica lens claims f/0.95 (theoretically it can be no larger than f/0.5), then it runs in steps which double every other step. it’s crucial to know that camera exposure doubles with each step: so from f/1.4 to f/2 is a doubling in exposure – and a halving in the opposite direction. Then f/2 to f/2.8 is another doubling. (Those comfortable with maths will realize that the sequence is due to the area of the aperture being proportional to square of the effective diameter, so each step must be a factor of square-root of 2, with rounding.)

T-number

This is an aside, because photographers will seldom come across the T-number scale. It is used in cinematography and technical photography, where it is usual for exposure metering to be done with a separate hand-held meter. It is the f/number adjusted to accurately reflect the amount of light which actually passes through the lens. Because all lenses absorb and reflect a portion of the light passing through the system, there is some loss of light, and complicated cine lenses commonly made of over a dozen groups of elements absorb a lot.

Exposure time

This is another favorite, which is why we already have an article about it.

As we explained there, we don’t talk about “shutter speed” and don’t even care too much for “shutter setting” as so many modern cameras, particularly those on cell/mobile phones, do not have a physical shutter. But we’re all interested in the duration of exposure or the length of exposure.

This scale has essentially no theoretical limits. It can be as long as days and be fractions of a millionth of a second. For really long exposures we simply hold the shutter open. For extremely brief exposures – shorter than can be given by shutters – we have to rely on brief flashes of light from flash-units: even in small cameras, the exposure time can be as short as 1/10,000 sec or shorter. In normal photography we generally work between about 1/30sec and 1/2000sec.

Ah! it’s that pesky forward slash again: here we’re dividing our shutter setting into 1: which is why photography professors call this measure “reciprocal seconds”. One second is 1/1 – one divided by one equals one, giving us a pretty long exposure. 1/10 is one second divided by ten parts, so each is a tenth of a second long. 1/1000 is one second divided into a thousand parts, so each is a very brief one-thousandth of a second slice of time. Of course in stills photography, we only take one slice at a time. And our cameras display just the lower (divisor) number, such as 1000, or 250.

It is natural, then, to talk of a “setting of 1000″. This means we set 1000 on our camera but we should know that it’s short-hand for 1/1000th of a second. Confusingly some people will talk about 1000-speed, but they’re talking about the ISO setting, not the shutter setting. (Another reason to give up talking about shutter speed.)

The shutter setting sequence is typically a doubling one, say from 1/2000 sec to 1/1000 sec exposure is doubled, then again from 1/1000 sec to 1/500 sec, doubling again from 1/500 sec to 1/250 sec, and so on. Each doubling step is one stop. I know it looks like it’s going the other way, but if you divide something into fewer parts, each part is actually larger than if you divided into lots of bits.

Notice something that is very, very important: the doubling step from 1/1000 sec to 1/500 sec is much, much smaller than the doubling step from, say, ½ sec to 1 sec. This reflects a fundamental feature of the nature of the way we, and systems such as photography, respond to light (it applies to sound and other forces too) and is a phenomenon of perception graced by a grand name: the Weber-Fechner Law.

Focal length

In the good old days, focal length presented no confusions. That’s because film formats were fairly fixed things. But first, what exactly is the focal length of a lens?

Let’s start by imagining your lens is a projector – in fact it is exactly that: it projects an image of the scene onto your camera’s sensor. It bundles the light from the scene into the lens, then sends it to the sensor: there is a point in the path of light where the image appears to come from – like the light fanning out of a film or transparency projector. This point goes by various technical names such as rear vertex or rear principal point, but the key thing is that we measure focal length from that point.

Now, we set up the lens to focus on a very distant subject (said to be “at infinity” because the light rays are for all purposes parallel to each other) and measure from the point from which the image appears to be projected in a straight line to the plane in which the sharp image lies – typically, that’s a shade below the physical surface of the sensor.

The point from which the image is projected can lie within the lens – we’d expect that. But this definition reveals the odd thing that the point from which the image is projected can also lie behind the lens and even in front. Look at a typical modern telephoto lens: its marked focal length is 300mm, but its physical length could be as short as 120mm or less. Similarly, you’re sure to have noticed that a wide-angle lens or focal length setting of 24mm is way longer than 24mm. Even the space between the rear of the lens to the sensor is greater than 24mm.

In short, focal length in photography has almost nothing to do with the actual physical length of the lens.

It’s always been the case that, in order to make full sense of the focal length of a lens, you needed another piece of information: the size of the format being used. So it’s always been that, in the film days, if you said “I’ve just bought a 75mm lens,” your photographer friends would ask you “For which format?” And on your reply would depend the feature of the lens we most want to know about: its field of view – how much of the scene it takes in.

A 75mm lens on the 35mm format is a moderate telephoto – ideal for intimate portraits. But on a roll-film 6×6 cam format, a suitable 75mm lens is a standard lens. Placed in front of a 5x4” film, however, a 75mm lens designed for the format gives an extremely wide angle view.

Equally so on digital cameras: if we have a tiny sensor measuring ½” across its diagonal, a 75mm lens produces a huge telephoto effect. The convention these days is to relate the actual, measured focal length of a lens to a focal length giving a field of view equivalent to that for the 35mm format. I’ve tried to introduce the qualifier term “35EFL” meaning “35mm equivalent focal length” so we say, for example, the actual focal length of the lens is 30mm so it is 35EFL: 45mm ” but it has not caught on (yet).

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Comments

1  

Millard

December 2, 2008 @ 4:38 pm

Pretty darn technical article I would say, but interesting read none the less. I will now have to change my blog posts to read F/1.4 and F/4. Thanks for the heads up on the technicals.

2  

Link Roundup 12-06-2008

December 6, 2008 @ 6:44 pm

[...] A Guide to Measurements in Photography – Part One i Digital Photo With all kinds of numbers and scales in photography, this guide lays out the essentials for understanding them. [...]

3  

Jeff Ball

April 5, 2009 @ 2:37 pm

Great information. Thanks for posting.

4  

Erick @ Photo Business Blog

July 8, 2009 @ 9:53 am

Nice review of the basics. Good explanation of the physical dynamics behind f/stops. E

5  

Richard

December 29, 2010 @ 12:01 pm

Michael Freeman (photographer and writer of many books on photography) makes a habit of refering to focal lengths as: …efl – makes sence, for the same reasons as the film days when I used to have a Pentax 6X7. Keep on pushng for efl or EFL…

6  

cyskin

August 28, 2011 @ 10:14 pm

Michael Freeman (photographer and writer of many books on photography) makes a habit of refering to focal lengths as: …efl

7  

Marie

December 12, 2011 @ 6:35 pm

Thanks for taking the time to delve into the definitions of photography measurements. When I first started taking digital pictures, I didn’t spend enough time on the basics and am glad that resources like this post exist to help folks avoid my mistakes!

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