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In a related thread, it's been debated whether there is a hard limitation to maximum possible lens aperture; it seems there is none. However, using the example of the nikon F mount, this technical appendix states otherwise.

My last assignment in optics reaches far back. What do you think of the schematics in the aforementioned link? Are they correct?

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If you have browsed through the technical pages of Pierre Toscani, you probably noticed he is quite knowledgeable when it comes to geometrical optics. Although I cannot ascertain his schematics are correct, I certainly trust him on this, as this is an extremely well researched article.

Concerning the maximum possible lens aperture, Toscani says that since the maximum angular aperture is about 54°, then the minimum f-number is about 1.1. At least I can confirm this logic is sound: if you apply the formula I derived in the linked thread, you get

1 / (2 sin(54°/2)) ≈ 1.10

If you use a tangent instead of a sine, you get 0.98 instead, which shows that M. Toscani is fully aware that one should use a sine instead of a tangent, since the second principal plane is actually a sphere (scroll down to the first figure).

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Agreeing with the answer in the thread you've linked, I don't believe there are hard limits for this. One day, one might invent a magical design or optical elements that would achieve unimaginable, super-large apertures.

But, as mentioned in that thread, there are so many soft limitations. Since the size of the back element, and the distance between the back element and the sensor/film is constant, you can only grow one way with the optical design. Take for example the famous Sigma 200-500mm f/2.8 lens. The sheer size and the price of this lens shows these "soft limits" in action. A wider-range focal length but smaller aperture 150-600mm f/5-6.3 lens from Sigma (just announced) is like a dwarf (both in price and size) compared to the 200-500mm.

To conclude, the soft limits are still so hard, that the real hard limits are not of big concern. Yet.

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