A question, specifically about digital SLR cameras:
How does the zoom specification on an attachable camera lens work in conjunction with the zoom specification of the camera’s lens?
For example, if I have a camera with 3x zoom potential and I attach a 3x zoom lens, what is the maximum zoom potential of the camera?
I’m asking because I’m in the market for a new camera–my old one has 18x zoom, which I love, but all the cameras I like (for other reasons) are things like 3x, 4x, etc.
Your question doesn’t make any sense.
What is “zoom potential?”
A camera’s zoom range is determined by the focal length range of the attached lens - if you have an 18-200mm lens, you have an approximate 11x zoom range.
Cameras also advertise “digital zoom”, but that’s crap, and should be avoided (you can do the same thing with any image editor).
Sorry, but your questions do not make much sense 
An SLR camera body has no zoom potential on it’s own. It depends entirely on the lens you put on it.
Also on SLRs they don’t usually measure zoom with numbers like 3x, 4x etc. because it is irrelevant on its own. Instead they use 35mm film camera equivalent focal length, eg. 18-55mm. So I am guessing the cameras you are looking at are compacts, not SLRs.
Please tell us the specific models of cameras you’re looking at so we can give you more relevant info.
Ok, maybe I understand what you’re talking about. Some compact cameras and videocameras have a thread where you can attach an extra lens like that.
In that case you multiply the two numbers. If the camera can do 4x zoom and the telephoto attachment 3x, then the resulting zoom will be 12x.
Zoom factor is just max focal length/min focal length. An 18x superzoom will be in 35mm fov terms a 35-630mm or possibly a 28-504mm. Lenses for dslr’s are named by their actual focal lengths, so if you want 35mm equivalent for a lens like an 18-200mm on “crop-format” dslr body you’d muliply by 1.5 (Nikon, Pentax, Sony), 1.6 (Canon), or 2 (Olympus) - which gets you to about 27-300. Unless you’re shooting with a full-frame dslr like a Canon 5D or a Nikon D700, but in that case I’d hope you wouldn’t be asking this sort of question. You won’t find any dslr lenses with the ridiculous 16-20x zoom factors some point and shoots are sporting. I believe the largest range is an 18-250mm (27-375mm equiv) made by Tamron for most common mounts.
If we’re talking about a teleconverter for a point and shoot, your zoom factor doesn’t change when you add the teleconverter. Your entire range shifts by the magnification factor of the TC. So a 3x zoom with a 35-105mm lens in 35mm terms would if you added a 2.5x TC become a 88-263mm equivalent, which is still a 3x zoom factor. You do multiply the focal length by the TC value, though, so if what you’re wondering is the maximum magnification it amounts to the same thing.
This is a common misconception. The markings on SLR lenses are always the lenses’ real focal length, which is a fixed property of a lens and does not change regardless of what it is mounted on.
To go back to the OP, it sounds like you have a superzoom point and shoot. Those aren’t DSLRs and you won’t be able to remove the lens and use it on something else. It’s permanently fixed to the camera.
Obviously Cleophus knows the topic but I thought I would amplify this by agreeing and also saying that nearly all lens reviews do quote a 35mm equivalent. This is because nearly all digital SLRs have a sensor that is smaller than a 35mm film frame. Therefore a lens such as a 50mm lens on a typical digital SLR will project an image that bleeds out over the edges of the sensor and produces a final image that looks similar to what you would get if you used a 75mm lens on a 35mm frame. So it is absolutely true that a focal length is a focal length is a focal length, no matter what camera you put it on, but the “equivalent” number gives an idea of what kind of image to expect if you have just spent the previous 50 years shooting 35mm.
BTW there are now SLRs available with a 35mm sensor size.
Didn’t someone (Olympus?) make a DSLR with a sensor GREATER than 24x36mm? (the image size on a standard frame of 35mm)
Well, Hasselblad makes some digital cameras with insane resolutions. And if you want one you better get a paper route.
Oh, bugger! Didn’t know that.
This explains why my Tamron 18-270 doesn’t look like a wide angle lens at 18mm. Turns out the equivalent focal length on my Cannon body is something like 29, not what I would call a wide angle.
Full frame DSLRs are coming down in price and are getting more common. Still, crop sensor cameras remain in the majority. But most lenses and reviews will start with the actual focal lengths and only mention the crop factor afterward. If you have a 1.6x crop camera you know that and take it into account.
Well what would you call it then? It is quite a bit wider than a standard (on 35mm) 50mm, and even a ‘true’ standard 43mm. In the days before zooms were so ubiquitous a common setup would have 28, 50 and 134mm.
My widest angle lens is a 10-20 mm zoom that I use on a Canon XT. That’s equivalent to 16-32 mm on a 35 mm camera, and is about a wide an angle as you can get without going fish-eye or something like that. 29 mm is moderately wide-angle.
Forgot to mention that a common category of these are sometimes called APS-C because they are the size of an APS film frame (same thing that is referred to by Telemark as 1.6x). I think Panasonic has their own unique size, and there is at least one other size out there. So it’s hardly standardized.
Panasonic and Olympus use a system called Four Thirds with a slightly smaller sensor than the APS-C cameras. The crop factor is 2, and the aspect ratio is 4:3 instead of 3:2. The new Micro Four Thirds uses the same sensor but a smaller lens mount and shorter flange distance, possible because the m4/3 cameras aren’t slrs and don’t have a mirror that has to be squeezed in between the mount and the shutter.