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In astronomy we use the same ratio to describe a telescope and call it a "focal ratio." My telescope is f/10 and thus has a focal ratio of 1:10. F-stop and f-number and all this other nonsense are just other shorthand versions. This is not the same as focal length (my f/10 has a 2000mm focal length and 200mm aperture).
Which is WHY it is f/10. 2000mm focal length / 200 mm aperture diameter = 2000/200 = f/10. Attached to a camera, it would act as 2000mm f/10 lens.
"Focal ratio" and f/stop are the same term. f/stop is the photographic use, where it is a variable on most lenses. Telescopes are fixed, typically do not have "stops".
Yeah, I realize that. Telescopes don't typically have the focal ratio quoted and must be calculated (or you'd have to dig pretty deep in the specs). The most important dimension in a telescope is the aperture. Only if you plan to use the scope for photography does the focal length and thus focal ratio really matter (although as I mentioned you need to know it to calculate FOV and magnification). The focal ratio doesn't really mean anything unless you want to understand the exposure settings you'd need on a camera. A typical conversation would be "what kind of scope do you have?" "I have a 6 inch Celestron" referring to the aperture. Whereas in photography you'll usually quote your lens as being "100mm f/1.8" referring to the focal length and focal ratio and ignoring the aperture (although it's indirectly reference with the f-number). You could just as easily get by quoting the focal length and aperture and just calculating the ratio for exposure (which is what we did in my high school photography class for whatever reason).