Why do zooms have small apertures even around 50mm?

Question

A 50mm f/1.8 prime from one of the major manufacturers can easily be found for $200 or less, but zooms that include 50mm in their range always seem to have much smaller apertures even at 50mm until you get into the thousands of dollars, and even then you're probably going to end up at f/2.8 at best. Is there a technical reason why a cheap 18-55mm kit lens can't be f/1.8 at 50mm and go down at the wide end?

My understanding is that 50mm is the simplest (and cheapest) focal length to design a fast lens for, at least based on prime lens prices; fast lenses that are any wider or more telephoto quickly become more expensive. Nikon's cheap 18-55mm zoom lens is f/3.5-5.6, but how difficult would it be to build an f/3.5-1.8 instead? That is, a lens that is f/3.5 at 18mm and f/1.8 at 50mm. I don't think I've ever seen a lens with a maximum aperture that grows when you increase the focal length, but it seems potentially reasonable when you start really wide (where a large aperture is presumably difficult to accomplish) and end around 50. Do any "reversed" non-constant aperture lenses exist? Is there something about the optical design that prevents this?

Answer 1

Update 2023: some of the elements of my answer below assume a DSLR, and in some cases mirrorless system make some of these issues less of a challenge. The points about zoom lenses requiring a more complex design are all still valid

A prime lens has a much simpler design, so for the same price, and weight, you can get larger lens elements and therefore a higher aperture.

However, there are some other factors to what you're asking. In the case of a 18-55 zoom lens, the lens has to have a retrofocal design, because at the wide end you are going down to much smaller effective focal length (18mm) than the physical distance between the lens and the sensor would otherwise allow. A retrofocal design means that many more lens elements are needed; it essentially is like combining a simple lens with a telephoto lens in reverse. A more complex lens has more elements, and to fit these into the available space they need to be certain sizes relative to each other, severely limiting the maximum aperture.

Now, a zoom lens uses the same lens elements throughout the zoom range: it does not "swap in" different elements depending on where you are in the zoom range. So a zoom lens that goes down to a wide angle (such as 18mm) must use the same number of lens elements even at the telephoto end, and throughout the zoom range.

Therefore, the limitation of maximum aperture imposed by the complex retrofocal design to permit wide-angle photography persists throughout the zoom range.

Additionally, remember that aperture is quoted relative to the focal length f, so getting a higher aperture number is harder as the focal length increases, which is why on a zoom lens you never see the aperture number improve as you zoom towards the telephoto, it always degrades (or is constant). That is, a zoom lens may be f/3.5-f/5.5 from wide to tele, but the numbers would never go in the opposite direction.

Answer 2

An f=50mm lens at f/1.8 aperture has an entrance pupil diameter of 58mm/1.8=32.2mm. This is the apparent diameter of the aperture as seen from the outside when viewed through the front lens element. A zoom lens will usually be designed with a focal length independent back part that admits as much light to the sensor as feasible (which usually includes the actual aperture with a physical opening size only depending on the aperture number), and a front part that can change its position and configuration based on the focal length setting. With a smaller focal length, the entrance aperture will look smaller when viewed through the front lens element groups.

There is no major optical recipe trickery that could upend those basic relations to a degree where you'd end up with more magnification for the entrance pupil than proportionality to the focal length would imply.

So the larger your focal length range ends up, the less feasible it becomes to get close to the performance of a prime lens that can utilise all of its light paths and optical corrections without consideration for other focal lengths.