• Focal Length controls the field of view in front of the lens. A longer focal length has a narrower field of view than a shorter one. Behind the lens, it is designed to project this image to a certain size and distance, as given by camera mount specifications. So we perceive this narrower field of view as having more "reach" as you can see farther into the distance. In layman terms this is called "zooming" - when you achieve more reach. Probably many would only call it zooming if it extends the visual range, and also if you achieve it from a 400mm telephoto lens. It is quite linear(*). Double focal length , half width and height of the target in front of you.

• Zoom in the camera lens/objective world is given when a lens can change its focal length. It is the factor given by max focal length to min focal length. 55/18 = 3X in a standard lens. 2X in a 10-20mm superwide. Compared to the visual field of view, mnany people might not perceive that as zooming in on the target, exept for the person looking through the viewfinder at 10mm for a long time and then switching to 20mm. The " ultra-zooming" 400mm, has no zoom at all, unless you call 1X a zoom, since 1 is also a number.

• Magnification is the ratio between subject size and projection size on the sensor - in the natural world; we are not going digital in this. The word can feel misleading as most lenses we use are below 1X - very much so. In common usage we are talking 0.0001-0.1X Your 1 inch quarter will be 1 inch on the sensor if you use a 1:1 macro lens at minimum focus distance. That requires a medium frame camera to frame it. But, wow, you will certainly capture the details on that one. If you move farther away, the magnification will fall off. Double distance, half magnification. Sounds familiar? The FOV is the same, unlike focal distance, but the effect is similar but inverse. In a 2X zoom you can change magnification, ie. the size projected to the sensor, by a factor 2. The wide sigma 10-20mm can do this. The 10mm magnification of that beautiful landscape will start out very very small though. At at 24meters it is 0.00042X. From there you can now "zoom it" to 0.00085X. The 400mm which cant zoom at all instead have 0.017X of the same scene. But in practice it is 40X better magnification o reach compared to the 10mm.

So focal length, magnification and distance are absolute terms, while zoom is relative.

(*) Linear as long the distance is significantly higher than the focal length