Why are certain apertures so popular?

Question

Popular f stops in lenses are typically f/1.2, f/1.4, and f/1.8 for portrait lenses. The reasoning behind that is pretty self explanatory.

Moving up past 1.8, I see some f/2.2 lenses occasionally, but I feel like f/2.8 lenses are very popular. I never really learned why, but I'd figure it's probably because f/2.8 is a good balance between adequate DoF, sharpness, and bokeh for most general purposes.

Moving up from f/2.8, I see some stock lenses at f/3.5, but what's really popular is f/4. I can't really seem to figure whats so special with f/4. What's the big deal with f/4 that makes it so popular?

Edit: to clarify what I mean by "popular", I did a simple search for slr lenses on B&H Photo Video and filtered the search by maximum aperture. The website lists 241 f/2.8 lenses, 114 f/1.4 lenses, 79 f/2.0 lenses, and 64 f/4.0 lenses. Other apertures like 6.3, 4.5, 3.2, 2.9, 2.4, and 1.6 have less than ten listed.

Answer 1

I think this is pretty simple. Fast exposure math in photography today is based around the concept of a stop. The aperture stops — the f/stop scale — follow a progression roughly along the powers of the square root of 2 (simply because increasing diameter of a circle by that factor doubles its area).

f/1 is quite rare (because it's ridiculously expensive to make a lens with anything approaching decent image quality when the aperture is as wide as the focal length). The next stops are f/1.4, f/2, f/2.8, f/4, and f/5.6.

Lens designs are clustered around these maximum apertures simply because it's just simpler to start at a full-stop increment. On lenses with a physical aperture ring and actual "stop" clicks, starting at a full stop is easy and convenient. And, differences of less than a stop aren't hugely significant. Other than that, it's mostly just habit. If you're a lens-maker deciding to design and market a lens, the full stops make natural categories to slot into.

Of course, as you've observed, this isn't a general rule, and there are plenty of lenses with max apertures of f/1.2, f/1.7, f/1.8, and f/2.2 — not to mention f/3.5 on consumer zooms.

Answer 2

The short answer is f/4 gathers half of the light as f/2.8, f/2.8 gathers half of the light as f/2, and f/2 gathers half of the light as f/1.4.

Lenses manufacturers want to make it so since the shutter speeds are also half of each other per step (1/1000, 1/500, 1/250, etc).

This makes it easy in the film era where one has to determine an exposure level first, then choose the aperture for each shot. Say according to my light meter f/2.8 paired with 1/250 (with given ISO on the film, of course) gives me the right exposure, then if I now want a larger aperture f/2 for my portrait, I would just set the shutter speed to be 1/500 to balance off the excess light.

If you look at this vintage rangefinder, you would actually see the silver metal rings, one for aperture and one for shutter speed, are sticked together, so that it is easier for the user to change both of them by the same amount.

For stops between these common aperture levels, e.g f/2.2, f/2.4, f/3.5 etc, my guess is the largest aperture is limited by the physical size of the lenses. A large aperture brings more difficulty to the design hence lenses with large apertures are usually larger in size. Say the manufacturer wants to produce a small lens for portrait, they would be satisfied with something larger in size than a f/4, but something with f/2.8 is too large for them. So they pick some aperture level that gives them the right size, say f/3.5.

Of course all of this wouldn't matter today because the light meter can essentially determine the exposure at any given aperture size. The stops are still there for the above historical reasons.

Answer 3

Lens designs are created with a balance of trade-offs in cost, weight, audience, volume, etc. Some apertures tend to occur more often than others because they represent points of balanced trade-offs, and often because these are the best apertures a manufacturer can offer due to physics and size constraints.

At the most basic level, lens focal length divided by maximum aperture determines how big the front element needs to be, which then influences cost, weight, and potentially speed and/or ease of construction. A 50mm f/1.0 lens needs to have a front element at least 50mm wide to admit enough light, whereas a 50mm f/2.0 lens only needs a front element at least 25mm wide. This in turn means the inner elements will be proportionally smaller, and smaller lens elements drastically improve final weight and construction complexity. As a heuristic, the smaller the lens elements, the cheaper the lens will be to produce.

In addition to constraints by physics, sometimes the synergy of an entire lens line is considered. One such aspect is the filter ring size in front of a lens. One example of a well-considered line are the classic Nikon AI/AI-s lenses, where many of the lenses had a front filter thread of 52mm.

Here's a sample of focal lengths and maximum aperture, along with corresponding front-element minimum size. Note that all of them fall under 52mm, and you can find variants that have a 52mm filter thread.

Lens                    Front Element Min  
--                      --                 
Nikon 35mm f/1.4 AI     25.0mm             
Nikon 50mm f/1.2 AI     41.7mm             
Nikon 85mm f/1.8 AI     47.2mm            
Nikon 135mm f/3.5 AI    38.6mm             
Nikon 200mm f/4.0 AI    50.0mm             

In the autofocus/DSLR era, Nikon has moved on from the limits imposed by adhering to a 52mm filter thread size, and you will find that they and other camera manufacturers have lens offerings whose filter thread sizes tend to cluster around 67mm, 72mm, etc. Given the filter thread and focal length, you can often estimate with a good margin of error what the lens offering will be in terms of maximum aperture for most lenses between 15mm and 200mm.

At smaller apertures, the main constraint is often autofocus capabilities. Many camera bodies in the DSLR age to date have a hard autofocus sensitivity limit of f/5.6, f/7.1, or f/8, at which they will cease to autofocus, and some bodies have a mix of AF points that span that range of minimum aperture. When considering that AF availability is important in order to sell camera bodies in volume (and also provide ease-of-use), this limits the bottom end of a lens range.

For example, it is rare to find any enthusiast or consumer zoom lens that is slower than f/5.6 wide open. Because the front-element rule still applies for light gathering even for zooms, the short end will always have an equal or better maximum aperture on a zoom, and given the focal range for the zoom, you can see how many zooms cluster around f/4.5, f/3.5, and f/2.8 at the wide end (shortest focal length).

Finally, f/4 has one special property that makes it a hard limit for some lenses, particularly long/telephoto lenses. When using a lens with a teleconverter, every 1.4x multiplier on focal length costs one the same amount of maximum aperture light gathering capability. Thus, f/4 with a 1.4x teleconverter brings it to f/5.6; f/4 with a 2x teleconverter brings it to f/8. When combined with autofocus limits, it's no surprise that a lot of premium super-telephoto lenses are offered at f/4 or wider. Both Nikon and Canon have 500mm and 600mm f/4 offerings, 300mm and 400mm f/2.8 offerings, and 200mm f/2 offerings (or better, in the case of Canon). When combined with 2x teleconverters you will get 1000mm/1200mm @ f/8, 600mm/800mm @ f/5.6, and 400mm f/4. Similarly, only in very extreme cases will you find anything longer than 800mm (both Nikon and Canon offer a f/5.6 here). The weight and the cost of providing lenses beyond these apertures drastically narrows the potential range of customers that are willing to buy them, as well as those who can make effective use of their capabilities.