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When having a 50mm lens made for a APS-C camera its often the case that the lens has a focal length of 50mm on fullframe. However this means that you are getting something like a 75mm due to the crop factor.

I wondered, if you take a medium format camera and buy a medium format lens, like a 50mm Hasselblad, does this mean you have a wider image on the medium format camera due to the larger sensor (crop factor < 1) or would you get the same angle like a 50mm on fullframe?

I think crop factor is not the right term here but I think you get what I mean by that.

Crop factor is a characteristic of the camera, not the lens. A 50mm lens is 50mm no matter what you attach it to. The bigger or smaller sensor is what leads to crop factor, which is the ratio of the area of a full frame sensor to the area of the sensor in question. Smaller sensors will have a ratio > 1, and medium format sensors (or other larger sensors) would have a ratio < 1. It may seem a bit odd to call it a crop factor when it's less than one, though, at least semantically, since the result is a wider angle of view than what you'd get on a full frame, so it's more of an anti-crop factor.

The only reason that we even bother with this concept called "crop factor" is because of the absolute prevalence/dominance of 35mm film. Do you think the early shooters, big box view camera's in hand, were conceptualizing their lenses using a crop factor?

The focal length of the lens, such as 50mm, is a characteristic of the lens. This is considered the "normal" lens for 35mm format (What is a normal lens?) and it's one that we are all very used to using. But, when smaller digital formats became prevalent, with many people maintaining the use of their 35mm lenses on these formats, there needed to be a way to communicate to those people what the lens would "look like" on that format.

Enter the crop factor. An easy way to tell someone how their lens would look on a small format. You've been shooting 35mm for decades, know what a 35mm and 50mm and 85mm look like better than the back of your hand. Now you use an APS-C and you toss that 50mm on there and, because of knowing that it's a 1.5x crop factor, you know that your 50mm will "look" like a 75mm on that camera.

The exact thing holds up for medium format. Many, many people start with 35mm and then go up to shooting 120. Conceptualizing the lens use can still be done with the crop factor, it's just that instead of "cropping" you are actually getting more area captured. So, for example, the crop factor for 645 is roughly 0.62 going from 35mm to 120 in the 645 flavor. So, the 50mm lens on a 645 camera would appear to capture like a ~31mm lens on 35mm.

"Normal" by the way, becomes about ~75mm for 645. Take it out to large format - it's ~150mm for a 4"x5".

The key concept here is the conceptualization of the image that will be captured by a given lens on a different format.

Here is one way to think about this. Suppose we had a view camera (in simple terms - front and back rigid frames with removable boards connected with a bellows) that had three different backs - one for 35mm film, one for 120 film and one for 4x5 film - and was mounted on a sturdy tripod with a 90mm large format lens up front.

Then we focus, get an exposure and then take three pictures - one with each back. Note that the circle of light (the image circle) cast by the lens will be for all practical purposes the same for each shot, it is just the film that is changing. And the lens is just glass and metal, it can't know or react to what film is being used for each shot.

The shot with the 35mm film will have a slightly telephoto angle of view, the shot with the 120 film will have a more or less "normal" angle of view and the shot with the 4x5 film will have a wide angle view. But, take that 35mm frame and drop it in the middle of the 4x5 frame and the two images should match up. You could do the same for the 120 film frame.

If you wanted to you could get some cardboard and literally crop the 4x5 frame to give you the equivalent of either the 35mm frame or the 120 frame.

Also - If we made a 8x10 print of both the 35mm frame and the 4x5 sheet, we would have to enlarge the 35mm frame much more than we would have to enlarge the 4x5 film. We would expect this to affect the apparent depth of field in the two prints -- even though the images on the two pieces of film are more of less the same. This creates its own rabbit hole, as we've all seen large format portraits with very small depths of field. But while a 90mm lens would be great for a portrait on 35mm, you might use a 300mm lens on the 4x5 camera to get a similar angle of view.

I think because of the popularity of 35mm film just before digital photography, the term "crop factor" became a popular shorthand to describe the different angles of view you will get depending on your sensor size. Which, today, can be confusing.