I've never properly understood what the focal length of a modern camera lens really is. I'd bet that many amateur and even professional photographers don't either, even though we use the term all the time. This blog post is my attempt to get it straight in my own mind, at least in a simple enough way to help the rest of this series make sense.
While I wrote in my introduction that these articles would be short, this first one is longer than average because focal length is so important to understanding everything else about lenses and cameras.
Things were a little simpler in the pre-digital age, when most people were using 35 mm film, but those numbers are still unintuitive for most people. For those film cameras, and for the very few high-end modern digital single-lens reflex (SLR) cameras with so-called "full-frame" sensors, picture-taking enthusiasts know a few things:
But why is that? What is the focal length of a lens, and why does it have anything to do with how close or far from your subject you need to be in order to fit it in your picture?
For a simple, single-element lens, the focal length is the distance between the middle of the lens and the focal point, where parallel light rays get concentrated to a point. As a kid you might have tried burning paper (or, less kindly, insects) at the focal point of a magnifying glass, for example:
Things aren't quite so simple for camera lenses, because they're made not of one piece of glass, but of several glass elements stacked next to each other to allow for variable focusing, correct for distortions and aberrations, and so on. And usually they're not trying to focus sunlight to a burning point either; rather, they project an in-focus circular image onto the focal plane of the camera, which is where the digital sensor (or, formerly, strip of film) sits:
Photo above: With the lens removed, shutter open, and mirror flipped up, you can see right through the body of my Nikon F4 camera to the focal plane at the back, where the film would be.
All those extra pieces of glass result in all sorts of focal length ratios, indexes of refraction, and ultimately equations, which when you run the numbers spit out the focal length of the lens. But it's fundamentally the same basic idea as the focal length of a simple lens, and the way I like to think of it is this:
Similarly, in a 200 mm lens, the distance is 20 cm, or about 7.9 inches. In a 21 mm lens, that lens-to-sensor distance will be 21 mm, which is 2.1 cm (less than an inch), and so on*:
By the way, it turns out that when you focus closer than infinity, such as on a person a couple of metres away from the camera, the main lens element needs to move away from the film plane very slightly (usually only a millimetre or two for a normal lens) to keep the image sharp. So that's why you see lens elements move in and out when you turn the focus ring:
Photos above: My AF Nikkor f/1.8D lens at infinity focus (left) and closest focus (right). Notice how the lens element moves forward, away from the camera body (which would be on the right when attached) as you focus closer.
There are also lots of ways that lens designers use multiple glass elements in modern lenses so that the actual lens-to-sensor distance doesn't match the focal length (hence those equations I talked about a few paragraphs back).
But let's pretend they don't do that, okay? Because we still don't know why shorter focal lengths are wide angle and longer ones are telephoto, do we? Let's figure that out.
Imagine three lenses with different focal lengths: 200 mm, 50 mm, and 21 mm. Each has to bend incoming light a different amount:
Okay, we know (sort of) what's going on with the light behind the lens, inside the camera. What about the light the lens collected in front of the lens, before it got all bent? Let's extend my simplified mental picture of each lens to the left a bit, out to the subject of the photograph:
Follow the lines of the bent light backwards (to the left in my diagram), out to the subject for each lens:
The angle of the cone of light that each lens is sucking in is known as its angle of view or field of view. Imagine pointing each of those lenses at a city skyline:
The 21 mm lens will see the whole skyline: a wide-angle view. The 50 mm lens will see a few buildings, which is a normal view for your eyes. And the 200 mm lens might see a few floors of a single building: a telephoto view.
Ta da! Now you know why each type of lens has a certain focal length.
Okay, great, so a lens's angle of view depends on its focal length. Spiffy. You might be wondering a couple of other things, such as:
The answers to those questions require knowing more stuff, which is why next time we'll talk about apertures and f-numbers.
*SEMI-RELEVANT SIDE NOTE: From this simplified perspective, you can understand why some old fisheye super-wide lenses from the '60s, which had focal lengths of 8 mm or less, forced you to flip up the mirror inside the camera to use them. The rear lens element had to sit 8 mm (less than a third of an inch) from the film plane, so those lenses had to stick waaay back into the camera body—so far that they would hit the mirror and crack it if you didn't move it out of the way.
Newer fisheye lenses use multi-element design tricks to keep the rear lens element in front of the mirror and avoid that problem. But no, I don't know the math of how that works, so I'll just think of it as lens-design magic for now.
Some useful resources: