Depth of Field
"Depth of field", also known as "depth of focus" is how much distance, in front of and behind the spot on which you actually focus, is still in focus. In fact, there is not a particular point at which suddenly things go out of focus. If you're focused on something four feet away from you, something four feet and two inches away may not be in perfect focus, but the difference may be too small to notice. Something 30 feet away, on the other hand, may be so out of focus as to be unrecognizable.
In the following illustration we're looking at the light rays reflecting off a single point. It might be the head of a pin. Light rays reflect in many directions, some of which are caught by the camera's lens. those rays are bent such that they begin to converge. They converge at one point then diverge again.
When the focus ring on a camera lens is adjusted, the distance from the lens to the film is changing. That's all that's happening. If the distance from the lens to the film coincides with the point where all the rays of light have converged, that pin head is "in focus". But imagine that the lens-to-film distance is a bit shorter (or longer) than that. The light is not perfectly converged. Instead of creating a point of light, the rays create a blurry circle of light. This is called a "circle of confusion". The size of the circle varies in two ways. First, the further it is from the optimal focus point, the bigger it is. Second, the bigger the area that is collecting light, the bigger the circle is. A lens with a really big diameter will be bending light at steeper angles than a lens with a small diameter, so it will create bigger circles.
When you select a smaller f/stop on your lens (which has a bigger number), you are restricting the diameter of the lens that will gather light. Move your mouse over the illustration below to see what it looks like "stopped down". Notice that since the light is coming from a narrower angle, the circle of confusion is smaller.
In this illustration I show two separate film planes in order to show both the in-focus and an out-of-focus position. In your camera, the film plane remains constant but the lens moves. The light rays from a more distant object will come into focus closer to the lens than the rays from a closer object. When you turn the focusing ring, the lens moves forward or back, changing the distance between lens and film. For the purpose of this illustration it was much easier to show two film planes, but what I should have done in order to illustrate the out-of-focus position was to redraw the illustration with the lens moved toward the film, thereby making the cone reach a point behind the (fixed) film plane. But that would have required drawing lots more light rays, which would have been confusing. This illustration is optically accurate, even if it takes some liberties with what's going on in your camera.
Remember that in our illustration we're looking at a single point of light. Most things you photograph have many points of light, all of them right next to each other. Imagine having a bunch of pin heads all right next to each other, and having them not in focus. The circles will all overlap, creating a big blur. That's what you see through your camera.
Put simply, the longer the lens, the less depth of field at a given f/stop. I am not a mathematician and cannot explain the physics of it, but I can show you some examples.
Longer lenses tend to have larger f/stop numbers (indicating smaller openings) than smaller lenses. For example, the 560mm lens pictured below, on an 8x10 view camera, in spite of its enormous size, opens up only to f/11. It will stop down all the way to f/128 though!
*** This just in ***
The relationship between depth of field and lens size is not so simple. See this link for Michael Reichmann's demonstration of how depth of field is NOT a function of lens size. The difference between my tests and theirs is that they are moving the camera to maintain subject size, while I cropped the image (in the darkroom, as it were) to produce the same subject size. Note that in order to maintain subject size, Reichmann had to change camera positions, which means he changed distance ratios (see below). I would conclude from the combination of his and my tests that increased distance ratio decreases depth of field exactly proportionatly with reducing lens size increasing it. In other words, these two characteristics cancel each other out.
This one's pretty easy to illustrate. In the composite image below, the horizontal things are supposed to represent yards of distance.
From where the guy's standing, the dog is about 5 yards away and the sign is about 8 yards. The woman is only a yard from the dog and four yards from the sign. I've said before, I'm no mathematician, and I don't want to get bogged down with numbers here. If you like numbers, you can work out the ratios for yourself.
The point is that if she focuses on the dog, the sign's probably going to be out of focus, even at a small f/stop, but if the guy focuses on the dog, the sign may well be in focus, especially at a small f/stop. Why? Because the dog is relatively close to the sign from where the guy is, but the dog is way away from the sign from where the woman is. Even though the dog and sign haven't moved. Get it?
Click here for a discussion of depth of field in the context of a particular photograph.