Nikon, Canon and Sony make lenses in both full frame and crop sensor formats. Nikon labels their crop sensor lenses as DX. Canon labels their crop sensor lenses as EF-S and their full frame lenses as EF. Sony uses the FE label to designate their full frame lens.
Nikon and Sony allow the use of any of their modern lenses on either full frame or crop sensor cameras. However, when mounting a crop sensor lens on a full frame camera the lens will either vignette or cause the camera to switch into “crop” mode. The crop factor of the camera should be considered when figuring out the resulting effective field of view. For example a full frame 50mm lens on a camera with a 1.5 crop will have the field of view of a 75mm lens.
On a Canon, the EF-S lenses must never be used on a full frame Canon camera as they can cause damage to the lens, camera or both. EF lens can be used on either full frame or crop sensor cameras. Remember to calculate the crop factor.
When adapting older lenses designed for 35mm film to a mirrorless camera you’re in luck as most lenses designed for 35mm film are full frame. A few film cameras like the Olympus Pen series were half frame 35mm and the lenses are meant to fill a smaller image circle. They’re work on a crop sensor digital but most likely will vignette on a full frame.
Please also see THIS chart to find out if a specific Nikon lens will autofocus a particular Nikon camera.
Nikon makes a DX-format sensor and an FX-format sensor. The DX-format is the smaller sensor at 24x16mm; the larger FX-format sensor measures 36x24mm which is approximately the same size as 35mm film.
Different NIKKOR lenses are designed to accommodate the different camera sensor sizes. In the case of DX cameras with their smaller sensors, corresponding DX lenses have been designed, which are optimized for use with the DX sensor. The DX designation can be found in the lens name, i.e. AF-S DX Zoom-NIKKOR 12-24mm f/4G IF-ED. These lenses are smaller and lighter in weight and address the market's need for affordable, high-performance lenses with a variety of focal lengths and zoom options.
The DX sensor makes possible the production of lighter, smaller cameras, but because it covers a smaller portion of the image projected by the lens, a 1.5x crop factor (so called because the smaller sensor crops the image compared to an image from a 35mm