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Some digital cameras have lenses with a fixed maximum aperture. For example, f-2.8 or f-4.0. Other cameras have variable maximum apertures. This is usually marked on the camera or lens as f-3.5 - 5.6, or something similar. So what's going on here?
It's simply the need for affordable zoom lenses.
You see, the f-number is actually a ratio. It essentially compares how wide the lens opens to the focal length of the lens. For most people, that's a little confusing, so let's look at my favorite metaphor:
Let's say you're inside a huge cardboard box. You're sitting in a chair eight feet from the box's far wall and you want to read a book.
Now let's say I cut a 4" hole in that far wall. It isn't going to let a lot of light into an eight-foot box, is it? You probably wouldn't be able to read your book. But a three-foot hole in the side of the box would let in a lot more light. And then maybe you could read.
But let's say the box is only three feet long. In a box that short, you just may be able to read your book by the light from a 4" hole.
It's very much the same with lenses. The longer the lens, the wider it has to be able to open to admit a useful amount of light. And that can mean a lot of expensive glass. How expensive? Well, a Nikon 80 - 200 mm f-2.8 zoom lens will run you about $1,000 or more.
Imagine tacking a few hundred dollars onto the cost of a digital point-and-shoot camera. It would be an affordable option for a lot less people. And that's why digital camera manufacturers use variable maximum apertures: less glass and less cost.
So, when you see a camera with an f-3.5 - 5.6 (for example) lens, you know the zoom will be a lot faster at the wide-angle end than at the telephoto end. That's a good point to keep in mind when you're choosing your new digital camera.