This question already has an answer here:
If you abuse your lens by just stacking a bunch of extension rings one on top of the other, will this start to affect your image circle?
For instance, you have a lens that can just about cover your sensor with the image circle and you add a bunch of extension rings to focus up-close. Will the image circle start to show on your sensor or will it even widen? Or does it even matter?
Also, is it possible to express this relationship mathematically or does it depend on internal lens design too much?
Note: I ask about focused images, so I assume you still can focus on the object with all the extensions.