Martin, the watch hand actually does constitute a line pair. It is a dark line surrounded by light. The light on either side of the hand should have been diffracted into the dark area, and in fact the thickness of the hand should appear thinner in the final print than the original. Therefore, I would argue that to image that watch hand as accurately as is shown in Gigabit's sample photo, at least twice the resolution would be necessary than a first order calculation would indicate(posted 8745 days ago)
The ludicrous figure of 3000 lppm has never passed my fingers until now.Anyway. Now that we have Herr Gigabit's methodology, we can do some real calculation.
A 90mm lens at 50 metres is a reduction of 555 times. Divide a 0.5mm watch hand by 555 = 0.9microns. That's 1.8 microns per line pair, or 555 lppm! Multiply by 2.5 (the f number used apparently), and we arrive at almost the exact theoretical limit of resolution. What a coincidence! And that's several millimetres off-axis!
I'm surprised Vivitar haven't been flooded with orders for this miraculous lens, and by your formula for calculating film resolution, we find that the film can image an almost infinite number of line pairs per millimetre.Now, I for one, am more inclined to believe that a commercial company is telling lies, than I am to believe that a relatively cheap lens can perform at the very limits of theoretical resolution, off axis, at its maximum apeture. In fact I'm more inclined to believe in fairies. (Or at least their stories.)