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Light allowance, depth of field, speed and focal length. These are just some of the terms used when discussing aperture. Look at it this way for starters. Inside your lens is a ring that opens and closes to limit the amount of light allowed through to the film (or "chip" if we're talking digital), much like the pupil of your eye. Around the outside of the lens are numbers that range from f22 to f2.8, generally speaking, that control that ring.
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In terms of focal length, that is a discussion more of depth of field for the purpose of this article. The longer your lens (such as a 105mm vs a 24mm), the greater the range of control over depth of field you can have. If you open a long lens all the way up, the depth of field will be shallow. So let's talk a bit about what depth of field is. Well, it is much like it sounds. It is the range, or depth, of infinite focus. And, though photography is not three dimensional, you are kind of working with different planes. There are layers, rather than visible third dimensions. So when you are adjusting the aperture, not only are you adjusting the light allowance, you are also manipulating those planes. If you are doing a head shot with a 105mm lens you will want to shut the lens down as far as you can. Unless, of course, you only really want the eyes, and everything else on that same plane, in focus. The more in the shot you want in focus, the smaller the opening you will go for. And the opposite is true as well.
One of the greatest ways to learn and, more importantly, see what aperture settings can do is to play around with it. Use your standard 50mm lens on a 35mm SLR and take multiple pictures of the same thing. A still life is best for this exercise as it is less likely to be moved. And start by going from one extreme of f22 to f2.8 or wider, like f1.5 if possible, to see the dramatic differences. And once you start to get a handle on that (and then later the use of ISO ratings and shutter speeds), you will want to use your camera manually for the most part.
Questions, comments and suggestions are encouraged.