I agree with user86418's assessment that Jerry Coffin's answer has this backward, though he in turn seems to have conflated numerical aperture with ƒ/number.

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There are a number of zoom-lens “formulas,” but basically a telezoom changes the magnification (focal length) by moving elements in front of the aperture diaphragm.

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All zooms change the size of the virtual or effective aperture while zooming, "constant aperture" (really constant f-ratio) simply change the aperture enough to keep the aperture to focal length ratio the same. The design of "constant aperture" lenses is not radically different, just the degree to which the apparent aperture changes.

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Lens designers battle to solve a number of problems including chromatic aberration, distortion, sharpness and vignetting. With a zoom lens, this is all the more difficult because they have to solve these problems not just at a single focal length but throughout the entire zoom range. However, all lens design makes compromises simply because there are so many opposing forces. For a zoom lens, the lens designers decide what aperture they can get away with at each focal length in the zoom range, without too much softening or other issues such as vignetting.

Funnily, the (currently) accepted answer gets it completely wrong. Either that, or its terminology of "before the aperture" and "behind the aperture" is seen from the side of the sensor (which would not make a lot of sense) rather than the front lens.

It's clear that the aperture's physical diameter can be bigger in both cases. So, in either case, you would theorize that at the widest end you should be able to be f/2.0 or thereabouts and your sandbagging scenario would then apply to both. On the other hand, for the latter, the optics may be simplified and thus approaching prime quality in result. So... Tradeoffs.

Remember that when using an f-number to represent aperture, it's expressed as a fraction of the focal length, so as you zoom, the same aperture effective diameter is represented as a different number. f/2.8 at 20mm is half the aperture effective diameter of f/2.8 at 40mm. So your constant aperture zoom is not actually "maintaining the same aperture throughout the zoom range" as such. In fact, a 18-55 zoom which maintains the same aperture effective diameter throughout the zoom range would be something like f/3.5-10.7.

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To steal the numbers from John's answer (to save working them out again) the size of the virtual apertures for the two lenses mentioned are:

It's a matter of having the correct combination of concaved and convexed elements in place to reduce the lose of light throughout the zoom's range. While the f/4.0 might seem like your being cheated on the faster aperture, it's more a result of getting as sharp an image without chromatic aberration while keep a consistent timing and lighting throughout your zoom and focal range.

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Constant aperture zooms like the Canon EF 17-40mm f/4.0 L you mentioned make a different compromise; they put a lot more effort into getting a wider effective aperture at the telephoto end. As a result, though, they use more glass and create a heavier lens. Since everything is a compromise too, they don't want their effort into getting a wider aperture at the telephoto end to increase the softness or vignetting at the wide end, so that limits the wide end's maximum aperture. So you get a different balance of aperture sizes compared to the cheaper, lighter "variable" (in reality actually less variation in terms of actual aperture diameter) aperture zoom and all it really depends on is what sort of trade-offs have been made in the lens design.

This differs from our BX/CX Series which falls off in uniformity when configuring units larger than 16 inches in width but provide minimal edge effect and a thinner package.

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There is actually a fairly fundamental difference in the design. The diaphragm (the part that forms the aperture) in almost any lens is somewhere around the middle of the lens. In a fixed aperture zoom, only the elements behind the diaphragm move around to do the zooming. In a variable aperture zoom, elements both behind and ahead of the aperture move around to do the zooming.

Canon has some very good literature explaining all this, along with how Optical Diffraction is being used in some of their newer lenses to counter all the prior downsides to regular optics. I'll post it as soon as I find it again.

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There is no sandbagging going on in the constant aperture lens, at the wide end the lens is trying as hard as it can, it's just that it has been engineered to behave faster at the long end!

It's desirable for a zoom lens to have a much wider aperture effective diameter at the telephoto end than at the wide end, because as the image is magnified you need more light for the same amount to fall on the sensor/film. That is, you need it to be much wider just to reach the same f-number.

This is the principle behind constant aperture lenses, the size of the virtual aperture changes throughout the zoom range, despite the face the physical aperture clearly remains the same size.

My question is: are these good lenses sandbagging at the wider settings, or do they have a different optic system that allows them to maintain the same aperture throughout the zoom range?

Cheaper zoom lenses usually are faster at the wide end and slower at the long end (for example, the $150 Canon EF-S 18-55mm f/3.5-5.6). More expensive constant-aperture zoom lenses have the same aperture regardless (for example, $800 Canon EF 17-40mm f/4.0 L).

If the optics in the 18-55 made the virtual aperture 15mm at the long end it would be a constant aperture lens (@f/3.5) this would be very expensive however due to the [relatively] large zoom range, which is why as a cheap lens it remains f/5.6

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In a variable-aperture zoom ... elements in front of and behind the diaphragm move (and the diaphragm itself moves), so the entrance pupil doesn’t vary in proportion to the magnification, and the ƒ-number changes as you zoom the lens. (Note: Some zooms also may change the physical aperture diameter during zooming, as well.)

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My question is: are these good lenses sandbagging at the wider settings, or do they have a different optic system that allows them to maintain the same aperture throughout the zoom range?

When/if the elements in front of the aperture move around during zooming, you're changing the (effective) focal length of that part of the lens. You're then transmitting light through a fixed-diameter aperture, meaning the (effective) f/stop changes. Since it's only affected by the change in effective focal length of the elements in front of the diaphragm, the change doesn't (usually) correlate exactly to the change in overall effective focal length -- moving the elements behind the diaphragm changes the effective focal length without changing the effective aperture (e.g., my 28-135 has nearly a 5:1 zoom range, but the aperture only changes from f/4.0 to f/4.5).

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In any case, zooms have pretty complex construction involved, much more so than a prime lens ever would, and so there are a lot of considerations around optical correction at various focal lengths, the effect of the aperture on that correction, and so on. It may be, given the lens design and costs associated, that attempting get wider on the short end would result in a hugely unacceptable softness in the image or some other forms of abberation.

They have different optics and are usually substantially bigger lenses for the same focal range (compare a 70-200mm f/2.8 to a 70-300mm f/4.5-5.6 and see that the latter is small in comparison). To get the constant aperture at the long end, you need to have a bigger barrel because the aperture is a ratio versus the focal length. However, if you do the math for your examples:

So neither type of zoom lens really maintains the same aperture effective diameter. Note that the effective diameter is not necessarily the true diameter of the aperture ring, either, since part of the zooming effect is that the aperture ring itself is magnified. But the effective diameter is what is relevant.

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Simply put, the ratio f/4.0 means the effective size of the aperture is the focal length divided by 4 - for a 600mm f/4.0 this doesn't mean there is literally a 150mm hole where the aperture blades are, only that the lens behaves as if there is. (if you look at the design of the Canon 600 f/4.0 it's clear there isn't space for a 150mm opening in the middle of the lens).

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Finally, for certain there are different optical constructions between the two. Heck, there's different optical constructions between lenses of the same configuration but different manufacturers. It all comes down to cost versus benefit and, in the end, what price the market will bear for a lens of a given construction.

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At least in the usual case, the diameter of the aperture does not change as you zoom. This is fairly easy to verify -- take pictures at different zoom ratios and maximum aperture with some out of focus highlights. At least with your typical zoom lens, the out of focus highlights will remain round at all focal lengths, indicating that the aperture is remaining wide open (where it's round). Stop down the lens a few stops, and you'll start to see the shape from the aperture blades closing (though lenses with lots of blades, especially rounded ones, will retain nearly-round looking highlights somewhat more than others).

The entrance pupil, the image of the aperture opening as seen through the front lens, has a diameter proportional to the focal length when zooming with constant aperture number (which is what photographers work with and which usually corresponds to the opening size of the physical aperture blades). Obviously this change of the apparent size requires a change in lens elements between aperture and the front lens. This change will be sufficient for affecting the desired change in focal length at constant aperture number in simple designs; however a modern zoom lens contains quite more elements than just those responsible for determining the focal length: a lot of corrective elements are also involved. Whether any of the back groups move in addition to the front groups thus is a matter of the exact optical recipe.