Something I couldn't explain

[Kyle M.]

Kyle, I think you've either contradicted yourself in your response to my post, or maybe you misunderstood mine or the original poster's (unless I'm missing something). When speaking about the two lenses, you stated that "technically, the apertures will have a different diameter..." But the OP described both the Rapid Rectilinear and the Petval as having the same focal length of 200mm, set at the same f stop. Based on the formula you provided, which is correct, the diameters would be the same if the two lenses were set at the same f/stop, right?

Yes, I was thinking the OP was talking about two different focal length lenses in which case the apertures would be different diameter but a specific aperture would still give the same exposure with both lenses.

[Lens Carrier]

Thanks all...

[Emmanuel BIGLER]

I have plotted a schematic layout for a theoretical f/2.8 200 mm Petzval lens, thanks to the free software "oslo-edu" which is supplied with a Petzval demonstration model file.
oslo-edu can be downloaded from here https://oslo-edu.software.informer.com/6.6/

In this Petzval design, when the rear doublet has a diameter smaller than the front doublet, and if no additional waterhouse stop is added, the first doublet defines the actual aperture of the lens and its entrance pupil.
Hence in this case the diameter of the entrance pupil is easy to estimate since it is close to the diameter of the front doublet, for a 2.8 lens this yields about 200/2.8 ~= 72 mm.

The Petzval lens is supposed to be the oldest photographic lens that was actually computed.
Being a really thick lens, it is also one design which is exceedingly far from the model of a simple thin positive lens, where the pupils are located at the centre of the lens element, and for which the focal length is simply measured between the thin lens and the focal point.
In this particular Petzval design, the exit pupil is located in air about 366 mm in front of the first lens vertex and has a diameter of about 161 mm!!

Of course if you add a waterhouse stop in the middle of the Petzval lens, the pupils' size and position will change as well as the actual f-number. This could be easily computed with oslo-edu ... provided that you have access to the lens prescription!! Next time you buy a vintage Petzval, you should kindly ask the vendor to supply the lens with the list of radii, spacings, and glass specifications

Here for this Petzval lens, like any other Petzval design, the focal length has to be measured from the rear principal point H' (or rear nodal point N', they are the same for a lens used in air) which is located somewhere inside the lens, impossible to know where H'=N' is located without doing a simulation like here; or for an unknown old Petzval lens, in practice by using the "optical turnslide" method: when rotating the lens around H'=N', the image of a far-distant object focused on a fixed ground glass will not move. This allows to find H'=N' and determine the focal length H'F' without any prior knowledge of where H'=N' is located.