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I have a Nikon d7100, lens mount type F.
I sometimes happen to be at a vintage / second hand market where there are some lenses that I'd like to try.
I know autofocus and aperture might not work. It's ok: I just want to be reasonably sure that the lens can fit in the housing and the camera can shoot.
Is there an easy way to tell, by spotting some visual clues, that a lens will likely fit or will surely not fit on my camera?
It's not entirely clear, but I think you are asking how to tell if a lens is F-mount at all, and not whether a given variation of F-mount is compatible with your particular Nikon.
First of all, if the lens is branded "Nikkor" or "Nikon", then odds are that it's F-mount and will fit your camera unless it's a non-AI lens (more on that below). The two other common Nikon lens mounts are the S mount that rangefinders used and the CX mount that the Nikon 1 series cameras use. S-mount lenses look radically different from any F-mount lens, and to my eye it would be hard to mistake them as compatible with an F-mount camera. See this page for some pictures of S-mount lenses. CX-mount lenses are much smaller than F-mount ones, and their mounts are much smaller; there is no mistaking them for F-mount lenses.
If the lens is branded with the name of another camera maker (except Sigma), then it's not compatible. A few examples are Canon, Contax, Fuji, Fujifilm, Hasselblad, Leica, Mamiya, Minolta, Olympus, Panasonic, Pentax, Ricoh, Rollei, Sony, Yashica. I'm probably forgetting a big one or two.
That leaves third-party lenses, such as Sigma, Tamron, Tokina, Vivitar, Voigtlander, and Zeiss ones. I think their mounts should be labeled with the mount type, such as "N/AI" to mean Nikon AI (a variant of the F mount). If not, it's useful to know that the F-mount is physically the narrowest of the SLR mounts in common use, and so if you try to mount a non-Nikon-mount lens on your D7100, it should not even begin to fit without quite a bit of force, which you should not use.
Now, regarding incompatible F-mount lenses. If an F-mount lens has an aperture ring that is the same length (along the lens's axis) all the way around, it is a non-AI lens. If you try to mount such a lens, you can wind up breaking the AI follower tab on the camera's lens mount. The aperture ring on an AI lens has two arcs that are slightly longer than the rest of the ring. The longer of these arcs is called the AI coupling ridge, and it couples with the AI tab on the camera. See this page for an illustration. So, if the lens has an aperture ring at all, you'll want the ring to have these two sections that extend further toward the camera than the rest of the ring. On the other hand, if the lens has no aperture ring, it's a G-type lens, which will mount without a problem.
To get a complete picture of lens compatibility, you need to know the characteristics of both the camera and the lens. There are a number of tables on the Internet (one comes with your camera's manual), but here is Nikon's for your specific camera:
http://imaging.nikon.com/lineup/dslr/d7100/compatibility02.htm
Your camera looks to be compatible with most older lenses but can only be used in Manual or Aperture Priority modes with non-autofocusing lenses. You should tell your camera the lens focal length and maximum aperture for best metering (there is a menu for that). Very old lenses (before about 1977) won't mount and you shouldn't try to force them -- something could break.
[EDIT] If you want pictures, Ken Rockwell actually has a good set on his site, if you scroll down to the "Mechanical History" section of this page:
https://kenrockwell.com/nikon/nikortek.htm
Note -- Rockwell is a bird of a different feather, only rely on him for basic factual things, like his lens mount images and descriptions.
