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A 400mm f4.0 lens is supposed to have a maximum aperture diameter of 10cm. Looking at such a lens they don't seem big enough to fit that kind of aperture including all the mechanics for control inside them. Do modern lenses have a way of focusing light into a smaller aperture to behave like a bigger one or are they really always the size that the formula (fstop = focal length / aperture diameter) suggests?

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Your observations of the lens leads you to both a correct, and incorrect, conclusion.

  1. Correct: the aperture (i.e., mechanical iris) of the lens is substantially smaller than the 10 cm it supposedly should be. Only the front element is anywhere near 10 cm diameter. Where the iris mechanism is in the lens barrel, the diameter is substantially smaller than 10 cm.

  2. Incorrect: the stated aperture size is not actually 10 cm in diameter. In reality, it is the the apparent size of the wide-open aperture (the iris), when viewed through the front of the lens, that is 10 cm in diameter.

For any lens, the aperture when viewed through the front of the lens is known as the entrance pupil. It is the entrance pupil that is 10 cm in diameter.

See also:

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    \$\begingroup\$ That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much! \$\endgroup\$
    – LuLeBe
    Commented Mar 22, 2019 at 18:30
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    \$\begingroup\$ Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light. \$\endgroup\$
    – dmckee --- ex-moderator kitten
    Commented Mar 22, 2019 at 19:14
  • \$\begingroup\$ @dmckee Absolutely, great way of stating it from the iris's viewpoint! =) \$\endgroup\$
    – scottbb ♦
    Commented Mar 22, 2019 at 19:30
  • \$\begingroup\$ So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do. \$\endgroup\$
    – Ruslan
    Commented Mar 22, 2019 at 22:15
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    \$\begingroup\$ @bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more. \$\endgroup\$
    – Michael C
    Commented Mar 23, 2019 at 8:31
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Lens designers have a few tricks up their sleeves. As an example, zoom lenses change focal lengths but the aperture diameter does not physically change with the zoom. This is an oddity because as the focal length changes, so does image brightness. In fact, if the focal length is doubled, image brightness falls off 4X. Conversely, if the focal length halves, image brightness will increases 4X. How do you think the optician compensated and maintained the exposure? The front group of lens elements acts as a magnifier. In other words, the diameter of the iris as seen by the outside world appears expand and contract with the zoom when in fact it is fixed as to diameter. It is the apparent diameter of the iris and not the actual diameter that determines the light gathering power of the lens. Note: most inexpensive zooms give up the ghost as the user zooms towards max magnification. A more costly zoom will likely maintain a constant exposure throughout the zoom.

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    \$\begingroup\$ Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks! \$\endgroup\$
    – LuLeBe
    Commented Mar 22, 2019 at 17:26

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