Something I couldn't explain

[Lens Carrier]

Kids ask the best questions, and I didn't know how to answer one that I got from my teenage son the other day. He asked, "Why does it take the same amount of time to expose a photo with a little 8-inch (200mm) Rapid Rectilinear lens that has a diameter the size of a quarter, as it does to expose a photo with a big 8-inch (200 mm) Petzval lens that has a diameter the size of a can of soup, assuming they are set at the same f stop? Doesn't the bigger lens let in a lot more light? So why doesn't it need a shorter exposure?" he asked.

Um, well, hmm... I told him that I really hadn't thought of that before, and now that I had, I honestly couldn't explain why. So how might I explain this to a bright 17 year old (and myself as well)?

[Emmanuel BIGLER]

Hello from France !

The answer is easy: the Rapid Rectilinear with an overall diameter of about one inch (the US quarter dollar has a diameter of about 24 mm, according to wikipedia, since I do not have those coins handy here ;) ).
This makes a max aperture around f/8 for a 200 mm lens. 200/24 = 8.33

The Petzval lens has probably a much bigger max aperture. From memory I know that for the historical Voigtländer Petzval the max aperture is f/3.
The problem to demonstrate this to your son is that vintage lenses might not have modern f-stop engravings, but when both are closed to f/10, both will exhibit an entrance pupil diameter of 200/10 = 20 mm.
A lens with a 8 inch focal length, when opening at f/8, has an entrance pupil diameter of one inch.
A lens with a 8 inch focal length, when opening at f/3, has an entrance pupil diameter of 2" 2/3, ~= 68 mm.

If your son has some interest in geometrical optics, you can give him full details: it took a long time to early photographers to recognize that the actual diameter to be taken into account is not the the physical, mechanical aperture diameter which is located inside the lens, and also not the diameter of the front lens element, but the apparent diameter of the aperture as seen from the entrance side of the lens, i.e. the diameter of the image of the aperture given by the front lens group, called entrance pupil.
A rare lens where the entrance pupil is the actual physical aperture is Wollaston's landscape lens, where the aperture is in air at some distance in front of the lens which is a simple meniscus lens element.
Another photographic lens for which the entrance pupil is the actual physical aperture is Rodenstock's Imagon lens, a cemented doublet with the aperture in air, in front of the doublet.

[Mark Sawyer]

The larger lens loses its exposure advantage when stopped down. F/8 through a Petzval = f/8 through a Rapid Rectilinear. Same exposure times for any given situation.

[Mike in NY]

Since your son said, "assuming they are set at the same f stop," did you assume the opening for an f/8 Waterhouse stop for a Petzval lens would be larger than the opening of an iris stopped down to f/8 on the small RR lens? That wouldn't be the case. To build on what Emmanuel said, the reason the Petzval lens is so much bigger than the RR lens is because its maximum aperture is so much larger. The two lenses "start" with different apertures. If you built an RR lens with the same maximum aperture as the Petzval, it would become a much bigger lens.

[Kyle M.]

Since your son said, "assuming they are set at the same f stop," did you assume the opening for an f/8 Waterhouse stop for a Petzval lens would be larger than the opening of an iris stopped down to f/8 on the small RR lens? That wouldn't be the case. To build on what Emmanuel said, the reason the Petzval lens is so much bigger than the RR lens is because its maximum aperture is so much larger. The two lenses "start" with different apertures. If you built an RR lens with the same maximum aperture as the Petzval, it would become a much bigger lens.

Technically the apertures will have a different diameter, but aperture is aperture regardless of lens focal length. Aperture diameter is focal length divided by the f stop number. So f8 on say a 240mm lens would be a 30mm opening, on a 24mm lens it would be a 3mm opening. Different size iris opening but same exposure. As to how that all works I can't explain it.

[Bill Rolph]

Technically the apertures will have a different diameter, but aperture is aperture regardless of lens focal length. Aperture diameter is focal length divided by the f stop number. So f8 on say a 240mm lens would be a 30mm opening, on a 24mm lens it would be a 3mm opening. Different size iris opening but same exposure. As to how that all works I can't explain it.
The longer lens (with a larger diameter opening) will cast more total light than the shorter lens, but over a proportionally larger surface area. Thus the light intensity is the same for both lenses.

[Kyle M.]

The longer lens (with a larger diameter opening) will cast more total light than the shorter lens, but over a proportionally larger surface area. Thus the light intensity is the same for both lenses.

I sat and thought about it for a bit after that post and it started to make sense. But there's still a lot of stuff when it comes to lenses and their design that totally baffles me. So I generally confine myself to just using and enjoying them.

[Gary Beasley]

You might notice the f number is expressed as f/ or a fraction. Thats because it is a ratio of the measured aperture to the focal length and it was found long ago that this gave practically the same exposure for any lens at the same aperture. So a 100 mm lens at f/8 has a 12.5mm measured opening, a 50mm at f/8 a 6.25mm opening, but as the 100 is twice the focal length the aperture the film sees is the same size so the exposure is equivalent. If you want to get really picky theres T/stops which are calculated from actual light transmission values that take into account any light absorbtion by the glass and coatings.

[Wayne]

I sat and thought about it for a bit after that post and it started to make sense. But there's still a lot of stuff when it comes to lenses and their design that totally baffles me. So I generally confine myself to just using and enjoying them.

That's what they are for.

[Mike in NY]

Technically the apertures will have a different diameter, but aperture is aperture regardless of lens focal length. Aperture diameter is focal length divided by the f stop number. So f8 on say a 240mm lens would be a 30mm opening, on a 24mm lens it would be a 3mm opening. Different size iris opening but same exposure. As to how that all works I can't explain it.

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?

[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.