Are there lens with
1mm focal length?
What is the shortest focal length possible for full frame sensor? And can it be rectilinear lens?
Sigma EX 4,5mm, but it's for APS-C and still far from 1mm and it's fisheye lens, not rectilinear.
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Largely it depends on sensor size. 4.5mm is for APS-C but there are shorter ones, even less than 1mm, for smaller sensors.
The issue for a rectilinear lens is that as the angle-fo-view gets wider, the construction becomes more and more difficult. Remember that a rectilinear lens must preserve straight lines and so the optics will get more complex and certainly larger and heavier to correct for aberrations.
At this time, the largest field-of-view from a rectilinear lens on an APS-C camera is 104°, obtainable by at the widest of a Sigma 8-16mm lens. This was the widest of any rectilinear lens until last year when Irix introduced their 11mm and Canon followed with the EF 11-24mm F/4L that can achieve 126° field of view.
With a fisheye, the mapping is completely different and you can have some than even project more than 180°, up to 220° as far as I know, although I forget who was the manufacturer. It is a third-party one.
I you're talking about "full frame" there is the Nikon 6 mm fisheye (https://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/fisheyes/6mmf28.htm) and the rectilinear Voigtländer 10 mm for Leica M mount: https://voigtlaender.com/10-mm-f-5%2c6-hyper-wide-heliar-vm.html