The landscape of both cinematography and photography is littered with a wealth (or perhaps a glut) of choices in terms of “format”; the physical size of the imaging surface in the camera. You may be familiar with such diverse options as:
“Full Frame”
Super 35
APS-C
Micro 4/3
etc.
A tremendous amount of ambient confusion reigns regarding how differing focal lengths of lenses interact with format sizes to affect the field of view of the image. People use terms like “crop factor” to get a handle on how the expected field of view may differ between formats, but this often misleads novices into believing that one can simply use a lens “meant for” the format they’re shooting with (typically one of the smaller formats) and then they won’t have to consider the so-called crop factor and can get on with their lives.
The only way in which a lens can be “meant for” a particular format is if it has been engineered such that it projects a sufficiently large image circle across the imaging area to avoid vignetting (darkening of the sides and/or corners of the image). Focal length is a constant. A 50mm, for example, is always a 50mm, no matter what format it is projecting onto*. If we take Nikon’s naming conventions as an example, a 50mm lens sold for their DX (APS-C) system is only different from a 50mm sold for their FX (“full frame”) system in that the latter projects a larger image circle than the former.
“But!”, you may be tempted to respond, “if I put that 50mm FX lens on my DX body, I see a narrower field of view than I do on my FX body!” This is true, but it’s obvious that the lens hasn’t changed. What has changed is the area of the lens’ image circle which is being “sampled”, as it were, by the smaller-sized imager.
Consider this diagram, in which the 60mm-diameter image circle projected by the Leitz Thalia line of cinema lenses is overlaid on various common cinema formats:
What this illustrates is that as the format in question gets smaller, the angle of view produced by the combination of focal length and format size also gets smaller. It is clear that a Super 16mm-sized imager “sees” significantly less of the image circle than the Alexa 65’s does. Taking our Nikon example above, if you were to attach Nikon’s 50mm DX lens to an FX body, you would see the same angle of view as when you attach your FX 50mm but the image would be “portholed”; extremely heavily vignetted, like a Thalia is on a 15/70 IMAX frame.
So, whether a given lens is wide-angle or telephoto depends entirely on what size format it’s being paired with. Let’s presume the Thalia used in our diagram above has a focal length of 100mm. On a “full frame”** imager a 100mm lens produces a horizontal angle of view of 20.4°, which is fairly telephoto. When paired with the whole image area of the Alexa 65, however, a 100mm lens produces a 30.3° HAOV, which is more of a medium telephoto feel, much like what you would get if you mounted a 65mm lens on a “full frame” body.
That comparison I just made there is what people are getting at when they speak of “crop factor”. Where crop factor is practically useful is when one wishes to match angle of view across different formats. If I were shooting a scene with both an Alexa 65 and another Alexa with a Super-35 sized imager, and I wished to match HAOV on both cameras, it’s useful to know that the lens I use on my Super-35 body should have a focal length 0.46x that of the one I use on my Alexa 65.
*Focal length is the distance from the rear nodal point of the lens to the imaging plane when the lens is focused to infinity. The greater the focal length, the more magnification of the image projected on the image plane.
**I keep putting that in quotes because calling it “full frame” when one’s frame can be much more “full” seems silly, but we don’t have a better name unless we want to say “35mm stills” or “8-perf 35mm”.