frankchn wrote in post #16167556
The f-numbers that we all know and love is calculated by dividing the focal length of the lens over the width of the entrance pupil
of a lens. The entrance pupil is the optical image of the physical aperture stop as viewed from the front of the lens, and is limited in part by how big the front element is.
For instance, if the front element is 100mm in diameter, then when you look into the front of the lens at the aperture, the apparent size of the aperture (i.e. size of the entrance pupil) can only be at most 100mm. Hence, in most normal to telephoto designs, the size of the front element is directly related to the aperture (and focal length) of the lens.
This is true in practice - a theoretical 85mm f/1.2 should have an entrance pupil of 70.8mm, and the actual front element of the actual 85LII is approximately that wide (72mm front filter size). A theoretical 400mm f/2.8 should have a entrance pupil size of 143mm and the actual EF 400mm f/2.8L IS II has a lens hood diameter of 155mm (ET-155), which means that the front element should be about 145-150mm, again falling in line with our calculations. This breaks down somewhat when we talk about retrofocus designs (wide zooms like the 16-35 or 17-40, etc...), but that is another story for another time.
Having better coatings and such will improve the ultimate light transmission of a certain lens but has no effect on the the f-number. (If you are interested in the light transmission, then the T-number is what you should be looking up and what most cine lens manufacturers report).
A good reference on optical design is Hecht's Optics if you want to know more about this.
frankchn wrote in post #16167875
The 24-70s / 24-105s / 16-35s / 17-40s out there are at least partially retrofocus designs (in order to lengthen the lens so that the flange distance is appropriate for an SLR), which necessitates the large negative front elements to gather light from a wide angle and thus the usual relationship doesn't work too well. The use of large negative front elements in turn introduces aberrations that require a lot of glass to correct properly and a large aperture exacerbates those aberrations even further.
Systems with no mirrors to contend with has much smaller wide-angle lenses because they do not need to be so severely retrofocus (compare the 24L II against the Leica Summilux-M Asph 24). The optical design is often simpler as well.
It is quite an achievement for Canon to make the 24-70 to be as sharp as it is, and it was only achieved through exotic glass including 3 aspherical elements, 2 SuperUD and 1 UD element in a 18 element/13 group design. I personally think Sigma would have a hard time trying to come up with a design that is one stop faster(!) without introducing bigger and more elements, bringing them closer inline with the 70-200s in size and weight.
These are very good explanations. Thank you for summarizing and then expanding so concisely yet completely.
I started to come up with a response yesterday, demonstrating the size of the front element of the 70-200 2.8 as being pretty spot on for the needed f-ratio, but tripped over the very wide front elements of the 17-40 and 24-70 type designs, which, as you point out, are not a classical lens design. "Retro-focus" was the term I couldn't remember, and therefore couldn't explain. And then I needed to get back to work.
The relatively small front element of the 40mm f/2.8 pancake is a good example of the classic lens design front element size requirement for the designed aperture. It's a whole lot smaller than the front of the 17-40 f/4, which makes no sense at first glance.