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If you have any interest at all in using older Nikon lenses, you probably have some understanding of the difference between non-AI, AI, AI-S, AF and AF-S lenses. The trouble is that places on the web that explain the differences easily get lost in the details. This article is intended to serve as a slightly easier to digest version of the story.
A lens is a pretty simple thing. It takes light coming in at one end and bundles it so it can form an image on a piece of film or an image sensor at the other end. To do this well, the lens must be in focus and the lens opening (aperture) must be set to a useful size. So pretty much all older lenses have a focus ring, which usually moves the lens forward and backward to adjust the focus, and an aperture ring that sets the size of the effective lens opening.
If you think manual focussing is hard today, consider the plight of photographers who had to use a camera from the first half of the 20th century. With those, you don't actually look through the camera's lens, so basically you had to guess or measure the distance to your subject and then select that distance using the focus ring or lever. Those cameras also didn't have light meters. But film is relatively forgiving, so outside during the day it's entirely doable to set your exposure based on the time of day and the weather, starting with the sunny 16 rule. Until the 1990s film often came with an exposure guide printed on the box. So you just set the aperture and the shutter time and you're ready to shoot.
With the single lens reflex (SLR) camera, you actually look through the lens and see the image that will be captured by the film or sensor when you press the shutter button. This makes focussing a breeze: just turn the focus ring until the image is sharp! Photography has never been this easy. Of course with your aperture at f/16 in accordance to the sunny 16 rule, the viewfinder image gets rather dim: f/16 lets in only 1.5% of the light that f/2 lets in. SLR makers solved this by keeping the aperture at maximum so the image in the viewfinder is nice and bright, and then quickly closing down the aperture to the selected value when the shutter is pressed. And life was good.
Then came along the next innovation: light meters. A separate light meter tells you how much light falls on the meter. Which is not so helpful when shooting something a little or a long ways away. You also have to adjust manually for filters and special lens behavior, for instance, with macro photography. So light meters were put inside the camera where they could measure the light through the lens (TTL).
However, keeping the aperture open until the shot is taken now starts to complicate matters. If we're still on f/16 on our sunny day, we'd expect the camera's light meter to indicate a shutter time of around 1/125 using 125 ASA (ISO) film. But the lens is still wide open at f/2 at this point. So the light meter needs to take into account the difference between the aperture of the lens wide open and the aperture setting that will be used to take the shot. Which gets us to...
Nikon uses the name "Nikkor" for its lenses. The lenses that Nikon used on its F-mount SLR cameras between 1959 and 1977 have a little fork or "rabbit ears" on the aperture ring. The camera has a pin that rests between the tines of the fork so it can keep track of the position of the aperture ring.
When mounting a lens, obviously the pin had to be inserted in the fork and it was also necessary to turn the aperture ring all the way in both directions so the camera could learn the maximum aperture.
The newest cameras that work like this are now more than 35 years old, so this meter coupling system is very, very obsolete. Later cameras that are made for AI/AI-S lenses (up next) may be damaged if you mount one of these lenses, so don't use an unmodified non-AI lens on them. However, entry-level digital SLRs (DSLRs) such as the D3xxx and D5xxx series can mount these lenses just fine, although those cameras then operate without their light meter. These lenses also work with many non-Nikon cameras through an adapter.
When Nikon introduced the AI system, the company would convert older lenses to the new system for a modest price. There are still a few places that perform this conversion with different levels of finesse, but if you have a nice unconverted non-AI F-mount lens, it's probably worth more in its original state.
In 1977, Nikon came up with a new way to couple the aperture ring to the camera's light meter: Auto Indexing or AI. AI lenses have a ridge that catches a feeler on a ring surrounding the lens mount on the camera. (Mounting a non-AI lens may bend or break the feeler.) AI lenses also have a mechanical system to indicate their maximum aperture to the camera, so now you just mount the lens and you can start shooting, the light meter has all the information that it needs.
AI lenses also have a second, smaller row of aperture numbers, allowing the photographer to see the selected aperture through the viewfinder. In order to let enough light fall on the aperture numbers, the rabbit ears now have a little hole on each side. The rabbit ears are no longer used, but for a long time Nikon kept including them on newer lenses for backward compatibility with older cameras. This video shows the differences between non-AI and AI/AI-S lenses:
Only a few years later, in 1981, Nikon improved the AI system to AI-S. It's not clear what the S stands for. The big difference between AI and AI-S is that the relationship between how much the camera moves the little lever that closes the aperture and how far the aperture closes is now standardized. This means the camera can control the aperture. Before AI-S, automatic exposure meant that the photographer selected the aperture, and the camera would measure the light and select an appropriate shutter speed. (Aperture priority or A on the mode dial.) With AI-S lenses, shutter priority (S on the mode dial) is also possible, where the photographer selects the shutter time and the camera the aperture, or the camera selects both (program or P mode).
Ironically, even though modern cameras still use that same system with modern lenses, they 'll only work in A or M (manual) mode with AI and AI-S lenses, not S or P mode. This also means that modern cameras don't care about the difference between AI and AI-S: since you control the aperture through the aperture ring on the lens, they work exactly the same.
AI and AI-S lenses can be mounted on all Nikon cameras with an F-mount. However, lower-end cameras such as the D3xxx and D5xxx don't have the aperture feeler so you lose light metering. On the D7xxx and higher, you can use these lenses in A and M modes with light metering, but modern cameras lack the mechanism to determine the maximum aperture of these lenses, so you have to go into the menu and enter the focal length and maximum aperture under the "non-CPU lens" settings. The aperture selected with the aperture ring then shows up in the viewfinder and LCD display(s) as well as in the EXIF data, along with the focal length.
You may have noticed that AI and AI-S lenses have colored aperture numbers on the aperture ring. This helps determining the depth of field through the matching colored lines that indicate how far before and after the distance the focus ring is set to sharpness extends. On AI-S lenses, the highest aperture value is in orange.
In 1986, Nikon introduced autofocus (AF) lenses. This works though a little screwdriver that sticks out of the camera, which connects to a screw in the lens that is connected to the focus ring. With this, a motor in the camera can adjust the focus. The camera uses a number of focus sensors to determine whether different parts of the image are in focus and turns the screw accordingly.
All AF lenses also include a CPU. The camera communicates with the CPU in the lens electronically and learns the focal length and minimum aperture of the lens that way. This allows autofocus cameras to do their through the lens light metering and use S and P as well as A and M. (And AUTO.)
In order to manually focus an AF lens on an AF camera, you have to move the AF switch from AF to M. This retracts the screwdriver so it's possible to turn the focus ring freely. Lower end DSLRs such as the D3xxx and D5xxx don't have the focus motor, so on those cameras, AF lenses must always be focussed manually. Metering and program modes are not affected. On cameras without a focus motor or in manual focus mode, the autofocus system in the camera will still tell you if the image is in focus or not with the focus confirmation dot in the viewfinder. There are a few manual focus lenses that do have a CPU, those simply work like AF lenses in manual focus mode on AF/AF-S capable cameras.
Older models AF lenses are completely compatible with the AI-S system. The popular AF Nikkor 50mm f/1.8D, which is still sold new today, even has a couple of tiny indentations on the aperture ring where you would drill the holes for the screws to attach the rabbit ears so it can work on non-AI cameras! However, when used on an AF camera, the aperture must be set to the minimum. There's a little lock tab that keeps it there. The aperture is then set (manually or automatically) through the camera.
The D in model designations indicates that the lens can tell the camera the distance the focus is set to. This makes metering a little easier. At some point Nikon started building lenses that are no longer AI-S compatible. These are lenses with G in the name. Most notably, G lenses lack an aperture ring. All G lenses are also D lenses.
Although the original AF system works well and allows for smaller and lighter lenses, in 1998 Nikon introduced AF-S (not to be confused with autofocus single mode, also called AF-S). AF-S lenses have their own focus motor built in. Nikon uses ultrasonic motors, which they call "silent wave". Makers of third party AF-S compatible lenses such as Tamron, Tokina and Sigma have their own names for this type of motor. (Each company also has their own name for what Nikon calls VR, vibration reduction, which moves a lens element in real time to counteract camera movement during the exposure.)
Most F-mount film SLRs since 1990s (there are some exceptions such as the F55) and all digital SLRs can autofocus with AF-S lenses. Unlike the aperture ring, which is now pretty much a thing of the past, they all do have a manual focus ring. A switch on the lens itself switches between autofocus and manual focus.
On some (mostly cheaper) lenses this is a mechanical switch that disconnects the focus motor from the focus ring so the focus ring can be moved safely and easily. On these lenses, the focus ring rotates with autofocus, and the autofocus switch switches between A and M. Selecting manual focus through the camera will turn off autofocus but not release the motor from the focus ring.
On higher end Nikon lenses, the switch on the lens switches between M/A and M, where M/A means "autofocus but feel free to adjust focus manually at any time". Turning the focus ring doesn't stress the autofocus motor here, so with these lenses you can turn off autofocus with the switch on the camera or through the menu system and leave the switch on the lens in the M/A position. Of course moving the switch on the lens to the M position also turns off autofocus.
With older Nikon lenses, typically turning the focus ring all the way to the right sets focus to infinity. With newer lenses, this is usually not the case: they'll focus a little bit beyond infinity, so you have to use autofocus or manual focus to set the lens to infinity. With astrophotography, where there may not be enough light for the autofocus sensors, this can be a problem—although I've been able to use autofocus to focus on a bright star with an f/1.8 lens. To add insult to injury, many cheaper/smaller AF-S lenses no longer have a distance scale, so there's no way of knowing what distance the lens is focussed at.
35 mm film has an image area of 36 by 24 millimeters. All Nikon lenses until 2003 are designed to project an image that covers a piece of film or an image sensor that size. However, such large image sensors are expensive, so low and medium end DSLRs have smaller sensors, which Nikon calls DX. These are 24 by 16 millimeters (actually 23.5 by 15.6 mm on the D7100), or about a factor 1.5 smaller than a "full frame" FX sensor or 35 mm film. This means that a 50 mm lens on a DX camera produces the same angle of view as a 1.5 x 50 = 75 mm lens on an FX camera. Conversely, to get the same result as with a 50 mm on FX, you need a 35 mm lens on DX. (33 mm to be precise.) So DX is said to have a "1.5 x crop factor".
FX lenses work just fine on DX cameras, but the problem is that a wide angle lens isn't so wide with the effective focal length multiplied by 1.5. So in 2003 Nikon introduced lenses specially made for DX cameras, taking advantage of the fact that the image that the lens has to project is 1.5 times smaller than with FX. For the same or similar focal length or focal length range the DX version is typically cheaper than the FX version, if both are available.
DX lenses are not useful on film SLRs because the corners of the image will be dark or even black. FX DSLRs on the other hand, work fine with DX lenses. They simply switch to crop mode, where only the center area of their bigger sensor is used.
With a 55-year history, there are of course tons of additional details, exceptions, caveats and more. But the above is pretty what you need to know about Nikon lens compatibility before you go lens shopping. Good luck!