In this diagram f' represents the focal length, which as you can see is longer than the physical length of the lens assembly.

Focal length is not the distance from the rear element to the sensor, it's the distance of the nodal point of the objective lens to the plane of focus. In a simple system, the lens may have only one glass element and that's the real distance, but in a complex lens, the various elements are formed to make the physical lens much smaller (or sometimes longer for very short focal lengths) than the actual focal length and to work within the flange focal distance, so you can't physically see the focal length.

We use the flange distance to measure mechanically to the sensor plane. It is used for convenience in hardware fabrication. It's arbitrary according to the instrument/camera design, agreed between the client and the designer purely for manufacturing and has little relevance optically beyond that. That lets the lens manufacturing and the instrument manufacturing continue independently with the desired fitting of the two pieces, quite accurately, within a tolerance of acceptable error.

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If focal length is the measure between the rear element and the sensor then how can you have different flange focal distances? Is the focal length not literally the measure between the rear element and the sensor?

(This is more a comment than an answer, but I wanted to explain why the slightly-different other question I marked as a duplicate is really what you need to see, and this is long for a comment.)

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For example, by simply adding one more lens element, you can create a wide-angle lens with a focal length smaller than the distance between the sensor and any of its elements. This is a retrofocusing lens. This allows for smaller focal lengths than the flange-focal-distance length without the back of the lens protruding back into the camera body.

If you think about it for the moment, it's fairly obvious. Somebody with an 800mm lens does not have the rear element almost a meter from the camera sensor, the lens would be utterly monstrous (they are now, this would be much worse). So, there are obviously more complex systems at play here as a result.

In reality, complex lenses have multiple elements and this has the ability to shift the optical centre of the lens assembly.

The focal length is the distance between a hypothetical single-element lens and the sensor required to reproduce a given magnification of image. This is unrelated to the distance from the sensor to the flange. See this simplified example.

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We measure from that (rather relative) reference point with accurate instruments to place the various sensors or testers at the right anticipated place to test.

I order a lens, say. It arrives with a reference point machined into the barrel of the lens. The flange distance is the known distance to the image plane from the mounting point manufactured for the lens mount. Sometimes there is a thread or a bayonet mount to attach the lens to the camera/instrument body, sometimes lens clamps must be used in a laboratory setting for large/heavy lenses such as scanners, process lenses, or plotters.

Interestingly, this concept of extending the focal length can be taken to an even greater extreme with a mirror lens, where mirrors further extend the travel distance of the light and hence the focal length without actually increasing the physical size of the lens.

You ask "Is the focal length not literally the measure between the rear element and the sensor?", and the rest of the question hinges on that. In fact, no, focal length is not that measure.

If we only used lenses with a single element, the focal length stated would always equal the distance between that lens element and the sensor.

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In the same way, but the opposite way around, a telephoto lens is capable of having a focal length that is longer than the actual length of the lens. In these multi-element lenses, the optical centre of the lens is outside the front of the lens assembly.

Thus, a lens with a 600mm focal length would need to extend about two feet in front of the camera body. And a lens with an 18mm focal length would need its lens element positioned only 18mm from the sensor. Clearly in an SLR camera this is impossible, as it would extend too far inside the camera.

Focal length is measured from the "optical center" of the lens (technically, the "rear nodal point" when the lens is focused at infinity. (More about this here.) If you imagine that the multiple elements of a modern complex lens "add up" to one imaginary single-glass lens, the focal length is measured from where that would be.

With a single-element lens, the optical centre is simply where that lens element is, but with more elements working against each other, you can shift that optical centre.