This is a very simple subject — complicated by people like me arguing about proper use of terminology, and people trying to explain differences that other people haven’t even noticed, and people pontificating on things they don’t adequately understand.
There’s nothing special about focal length in digital photography. The way a lens focuses light is completely independent of what the image is being projected on. The lens doesn’t know what’s behind it, and doesn’t care.
Why, then, do you so often read and hear the phrase “35mm-equivalent focal length” when discussing digital cameras? And what does it mean?
Essentially all experienced photographers are very familiar with 35mm photography; in particular, they know what they’d expect to see with a particular lens on a 35mm camera. They know it in terms of the focal length of the lens, not in terms of the angle of view.
In addition, the consumer P&S digital cameras have a range of sensor sizes. The view you capture through a particular lens depends on the lens focal length and the film/sensor size. So a 5mm focal length lens (yes, the sensors are that small, so the focal lengths are that short) gives a different view depending on the sensor in the particular camera. And all those small sensor sizes are unfamiliar to photographers and everybody else. So by stating the “35mm-equivalent” focal length instead of the real one, they’re giving numbers that are comparable across cameras, and that mean something to all experienced photographers.
People talk about the “focal-length multiplier” for digital SLRs — the Nikon models have a 1.5x multiplier, so your 50mm lens gives the same angle of view you’d get on a 35mm film camera with a 75mm lens. Some people will object strongly to the term “focal-length multiplier”, and they’re technically right, so to shut them up I often call it a “crop factor” instead.
“35mm-equivalent” focal lengths are convenient. But they’re not true. The actual focal length of the lens doesn’t change, that’s basic physics that doesn’t depend on what the lens is in front of. Why does it matter? It doesn’t matter very much most of the time. But when calculating depth of field, or bellows extension, you need to use the real physical focal length of the lens, not any of the other numbers that get thrown around. If you do everything on auto-exposure using through-the-lens metering, it won’t make much difference to you. But there are lots of kinds of photography where you can’t work that way all the time, and some of us have been doing photography long enough that we had to do those things fairly routinely. And many of us get hives when we see people misunderstanding things, even when the misunderstanding makes no difference to what most photographers do day-to-day. Call us anal if you like.
So, there you have it. Focal length isn’t changed by what camera you mount a lens on. The angle of view you see through the lens is changed by changing the size of the sensor or film the image is captured with.