Plate Beamsplitters - plate beam splitter
F-number lens
You know, I was going to argue lens mount and then I realized that I have a 200mm f/2.8 and the aperture on that is 71.4mm which is larger than the opening on my camera. So, I the only reason I can think of is cost...
The wider a maximum aperture, the more prevalent optical aberrations will tend to be (given a "simple" lens.) Wide aperture lenses become increasingly difficult to manufacture at reasonable cost, as you have to put more effort into correcting those optical aberrations. Additional lens elements are necessary to mitigate chromatic aberration (which can become quite horrendous at apertures wider than f/2), correct for distortions (to maintain rectilinear behavior and minimize distortion effects), correct for spherical aberration and the focus shifts that result from it (or, leave the spherical aberration in, and correct for focus shift with additional electronic intelligence), etc.
Aperture f numbercanon
To get the advantages of an aperture wider than the mount diameter, the maker has to be doing some extra work with the rear elements and that will cost. This becomes a cost benefit analysis because they aren't going to expend the effort on a lens that will then cost so much that almost nobody will buy it (happens every now and then, Google the Canon 5200mm lens). They have to ask, what does the extra light really give on any given lens? I think, for the most part, once you're in to the 1:1 ratio of aperture to focal length, the answer is not a lot, or at least not a enough to justify.
You'd have to have a very good reason to go faster, "to take better pictures indoors without flash" doesn't quite do it. It has to be something like "I'm going to walk on the surface of the moon for the very first time"...
Carl Zeiss Super-Q-Gigantar 0.33/40mm (c. 1960) This is the world's fastest lens ever made, for Contarex Bullseye. Unique lens made by Carl Zeiss for Public Relation purposes - ex Barringer Collection.
f-stop photography
Aperture f numberphotography
As to how they can squeeze the benefit of an aperture larger than the mount, well, I'm not a physicist or a lens maker... I'll leave that to people smarter than I. Mind you, I suspect that there is a limit to how big an opening you can get for a given focal length, regardless, but how to arrive at that, I don't know.
Why do you feel hot when you wear black clothes? While black objects absorb the energy from all colors and become hot, the objects gradually release some of that energy back into the air around it. Your body receives part of the heat energy that the black clothing radiates.
At the moment it is on auction at Westlicht-Auction. Since I am not sure if I am allowed to link to such a page here is the description:
Meera Chandrasekhar, a curators' teaching professor of physics and astronomy at the University of Missouri, says, "Light is a form of energy. The energy comes to the Earth from the sun through electromagnetic waves." The human eye can detect what scientists call visible light, which is only a small slice of a broad range of electromagnetic waves, called the electromagnetic spectrum. Other forms of energy on this spectrum that humans cannot see include infrared (also called heat) and UV light.
Combined with the necessity of correcting the increasing effects of optical aberrations, faster lenses require larger elements, more glass, in more groups, with more moving groups, to achieve usable quality at wide apertures. That amounts to tremendous cost, requiring prices that are out of range for most photographers. When it comes to a manufacturer like Zeiss, the creation of an f/0.7 lens (the fastest camera lens on earth, as far as I know), it is probably more of a prestige thing than a money maker...the best lens maker on earth had better have the best lenses in all cases, right? ;)
F-number calculator
To better understand light waves, Chandrasekhar suggests wearing diffraction grating glasses. Examine different light sources, such as LED versus fluorescent bulbs, and compare what you see. Be sure to never look directly into the sun, even with your glasses, as the light can damage your eyes.
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I am not really sure if this monster ever produced pictures, because there are simply no samples around. Everybody seemed to make pictures OF the lens, but not with it :-)
F-stop vsaperture
f-number formula
How light interacts with objects determines what we see. Light rays that come from a source such as the sun reflect off items and enter our eye. Chandrasekhar explains: "When the energy is taken up by the object, it's called absorption, and when" the energy "is bounced back by" the object, "it's called reflection." Objects are selective about which colors they will absorb or reflect. "A black object is black because it's absorbing all the light; it's not reflecting any color," Chandrasekhar says. White objects reflect all color.
Working f-number
Another that's probably more meaningful for most practical purposes is that your depth of field would nearly evaporate into none at all. Just for example, consider a shot with a 50 mm lens from around 3 feet away -- a more or less typical head/shoulders type of shot. At f/1.0, your DoF is already down to 3/4ths of an inch. At f/0.5, it would be approximately 3/8ths of an inch -- if, for example, you focused on somebody's eye lashes, the eye itself would be noticeably blurred (or vice versa).
I guess if your primary ambition is to shoot pictures of stamps under glass at night, the minimal DoF wouldn't be a problem -- but for most subjects, using it well would be challenging.
There is a Zeiss Lens called "Carl Zeiss Super-Q-Gigantar 0.33/40mm" Yes it got a max aperture of f/0.33 and therefore is the fastest lens ever made.
Lenses faster than f/1.0 exist but the prices skyrocket once you get below 1.0 as you're close to the limit of how far glass can actually bend incoming light! Tolerances become very tight and manufacture is expensive. The limit is around f/0.5 for glass (which has a refractive index of 1.5) to go faster you'd need to use a more exotic material such as quartz or sapphire, pushing the cost even further. I once read a thread online where someone calculated you could.make an f/0.25 lens but it would have to be built entirely out of diamond...
The fastest lens I've ever heard of was f/0.55, almost two stops faster than Canon's legendary f/1.0! They are used for lithographic etching of silicon wafers and the aperture is required to avoid diffraction limiting the resolution. The same effect that causes soft images with DSLRs at f/16 starts to occur at wider and wider apertures as you try to extract more detail.
It should also be noted that a larger f/# must maintain the ratio of light allowed with other similar lenses. An f/0.9 lens must allow 1.5 more stops (more than 2x as much light) than an f/1.4 lens, and the physical size of the aperture to achieve that often requires a larger lens barrel diameter. Increasing the barrel diameter requires, at the very least, a larger front element, which can quickly add to the cost of a lens. An f/0.5 lens must allow nearly 3 stops more light through as an f/1.4 lens (a volume of 8x greater light), and requires a physical aperture that has a diameter 2.8 times larger. Note that it is important to remember that the physical aperture size as calculated from relative aperture is only as viewed through the front lens element (which tends to magnify the innards a bit.) The true physical size of the aperture is usually not quite that large, however lenses with particularly large maximum apertures beyond f/1 do generally necessitate a bulky lens barrel. It is possible to correct for an aperture larger than the mount with more optics...but thats part of where the added cost of wider apertures comes into play.
(As it turns out, Zeiss pretty much does, given their superb optics, and between having the fastest 50mm f/0.7 lens, and the longest at and clearest telephoto lens with their Apo Sonnar T* 1700mm f/4 lens...and believe me, a 1700mm f/4 is almost as insane as a 50mm f/0.7...thats a TON of light for such a long focal length!)