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ATM f ratio



Excuse the ignorance   -   but...
What are the differences between mirrors with a high f ratio vs mirrors with a low f ratio?  I know the lower the f, the shorter the focal length.  That part's easy.  The thing I don't get is: So what?  If I have an 8" mirror that I figure for f20, how will it perform differently than one figured for f4?  Does the focal length affect the apparent size of the images? Is that the same as magnification?  If not, does it affect the AFOV?
Oh, so confused..
TIA - Andy Mail