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Difference Between Digital Zoom and Optical Zoom
Illustrated with some pictures taken in Boquete, Panama!
There's a big difference between optical zoom and digital zoom, and they work by entirely different principles. Optical Zoom is a matter of having a zoom lens, which is like a variable telescope. Digital Zoom is effectively image trimming, cutting a piece out of the middle of a larger image!
Part of the problem with this is the way you see so many fancy adverts for digital this and digital that, and anything "digital" has a salesmanlike advantage up-front in that it sounds modern. Well, don't be fooled by "digital zoom", as it a poor alternative to optical zoom!
Be wary of specifications that claim 1000x digital zoom, or other arbitrary factor. Digital Zoom is not real. The effect is achieved by the camera cutting down the image internally, like taking a sheet of newspaper and using scissors to cut a postage-stamp sized piece out of the middle. If you want to do that, you'd be better off doing it yourself in your computer (post processing). That way, you have control of it, after the fact. For example, this picture of a humming bird was taken by cutting a piece out of a much larger photo which I took and then post-processed. (Note that this effect can't generally be achieved by digital zoom, because of the difficulty of holding the camera still enough and/or aiming at a moving target!).
In contrast, Optical Zoom is inbuilt telescopy. The real optics behaving like a telescope. For example, in the FinePix (Fuji S5700) camera, which is not an expensive camera, the fact that it has 10X optical zoom easily makes up for the relatively low megapixels in relation to more expensive cameras. In the first picture seen here, at the top, there's a landscape in Boquete in the highlands of Panama. Now take a look at those trees in the distance on the top of that hill. With the same camera, taken from the same spot, but with the optical zoom turned right up to full, we get the second picture...
The point about this is that it's done entirely optically, so both pictures are the same resolution. They are both the same size in megapixels. If this had been digital zoom, the second picture would have been just a tiny piece cut out of the first picture, and would essentially be a low-resolution picture.
An additional point about optical zoom is that you can zoom all the way in optically and take a high-resolution picture, and then digitally zoom in and look at the interesting bits in the middle. As this is being done after the fact, it's possible to achieve much better precision. The original high-resolution pictures are preserved.
Now bearing in mind that these pictures were taken over six months ago, and the camera has optical zoom and no digital zoom, it's still possible to digitally zoom in on the top of that tree on the left there and get a close-up of the pine needles on the top! Like this...
As I was saying, the Fuji S5700 FinePix is not an expensive camera.