Aperture question

Hi all.

I've bene lurking for some time, and a couple of weeks ago, almost as an
impulse purchase, I got hold of an old MPP Mk VI, upgraded to Mk VII spec,
on eBay, which I've been having tremendous fun with (can play with it for
hours, even without taking any photos).

The camera came with a Schneider Xenar 150mm f/4.5 mounted in a Synchro
Compur. However, the pointer on the aperture slider was missing when I got
it, and the screw that used to hold it there was sheared off.

Eventually, I carefully managed to remove the old screw, and put a new
pointer on from a bust-up old Compur with a random 75mm triplet that I had
bene playing around with, and at that point I noticed that, when the
aperture slider is against the end-stop, the pointer goes a little beyond
f/32, which is the smallest marked aperture setting.

this got me wondering whether the aperture scale was off, or whether it was
actually going beyond f/32, so I unscrewed the rear lens group, leaving the
aperture blades "naked", closed the aperture all the way and measured the
width of the hole.

It came to around 2mm (not an exact measurement - it was done by eye by
holding a ruler over the hole, so it could be around 1/4 mm off in either
direction). Assuming that the aperture diameter is as implied by the
f-number, this suggests that the lens actually goes to around f/64.

Does this sound right, or is the actual relationship between aperture width
and f-number likely to be more complicated in reality than the simple
mathematical model implies?

It's quite common for a pointer to go past the last marked aperture
value. Lens makers mount their lenses on standard shutters, that is,
one will fit many.

The last mark is the lens maker's warning that the lens will not
perform well at smaller apertures. However, performance may still be
fine for small enlargements or contact prints.

Typically, the distance between aperture markings goes by the inverse
of the square root of two. So if you measure the distance between f22
and f32, as marked on your Compur shutter, the next value, f45, will be
about 0.7 times that distance past f32.

The simple optical formula for aperture, that is, the inverse of the
focal length divided by the diameter of the iris, works well for a
simple lens. But for complex, coated, lenses (and there may be many
other factors that affect light transmission) my experience is that it
won't work.The value needs to be multiplied by a factor, which you may
determine for your particular lens by measuring at a wider aperture,
say f5.6, and confirming it by measuring again at f8.

I have no proper proof for any of the above, just my long experience
with view lenses.