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If I shorten the focal length of a lens without taking any other measures, that will reduce the required flange distance for infinity focus - meaning that if the actual flange distance is not changed, the focus will be closer than infinity.

Is this effect used to achieve internal focus on prime lenses, and does it explain the effective focal length decreasing instead of increasing in such designs when focused closer?

In other words, do such lenses focus breathe BECAUSE you focus them, or do they focus breathe TO focus?

NOT asking about true cine lenses or floating-element ultrawides here.

(NB while this might seem like a pure optics design question not related to photography, it can become relevant when assessing how to best choose or modify lens adapters).

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I would have to say that they focus breath because you focus them.

It is due to changing the distance of the optical center (rear principal point) of the lens relative to the image plane, and it is not particular to IF lenses.

I believe the difference as to whether it causes an increase or decrease of the FOV depends on if the lens is of a telephoto design or retrofocus design (reverse telephoto). Also, there are other ways to affect focus such as moving rear elements.

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