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Zoom lenses and cameras with superzooms are often sold with a times ("×") zoom number — like a 12x zoom or 30x zoom. The question How do I convert lens focal length (mm) to x-times optical zoom? explains how this relates to focal length numbers, like 70-200mm or 18-55mm. But how does ×-zoom relate to magnification, when used for macro or just to make something far away look bigger?
How can two 70-200mm lenses have different magnification?
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
So of course we all know that when we zoom in on something, it appears to get bigger and takes up more of the viewfinder/camera sensor. However, I believe this question is asking about what is called magnification factor.
You most commonly see on this macro lenses where the whole point is to enlarge something that in real life is very small. The magnification is described like so:
original object size in real life:resulting object size on the sensor
So a lens with a 1:1 magnification factor would take an object that is 10mm across and project an image on the camera's sensor that is also 10mm long. A 1:2 factor would convert 10mm to 20mm. 1:3, 10mm to 30mm and so on.
(Note that a magnification factor of 1:3 can also be written as 3.0x. Also this factor is for a given minumum focusing distance. At other distances it won't have the same effect.)
A 1:1 magnification factor may not sound too great but when you think that today's camera's have on average about 18MP or so you can do quite a lot.
So why would two different lenses with the same focal length have different magnification factors? It really just ends up being differences in build quality and the actual purpose of the lens.
Feel free to comment. Hope this helps.
A numerical example
For years 35mm film cameras dominated. The image size was 24mm by 36mm.
let us assume we want a 20mm high image of a 2,0 m high object at a distance u in front of the camera. Provided u is at least 10 times bigger than the focal length f, the ratio of image height to object height is approximately f/u, thus
20mm/2m = f/u, hence we requite f = u * 10mm/ 1m
which gives
(wide) u = 2m f= 20mm; u = 4m f= 40mm; (telephoto) u= 10m f= 100mm
Modern cameras have a much smaller image screen, so one needs to have smaller images, and correspondingly smaller focal lengths to make objects occupy a similar fraction of the picture.
It requires less light to make a smaller image, so the diameter of the lenses can be smaller. This is why the iris settings on a camera is given as, f/ 4 ; f/5,6 etc f/4 means the iris diameter is quarter of focal length. The image will be equally bright for a 20mm lens of (stopped) diameter 5mm and a 60mm lens of (stopped) diameter 15mm .
