Why do they measure the distance between the lens and the subject when shooting a film?
David's good, but I don't see how. You did a fine job.I'm sure David will have a much more concise answer than mine!
The 1st Assistant Camera or focus puller measures the distance between the subject and the focal plane so that they can make marks on the follow focus and/or lens. Cine lenses (unlike stills lenses) have accurate distance markings on them, which allows the 1st AC to use distance markers to accurately focus on the start and end positions (for example) of an actor, and then estimate the positions in between. Even when markers can't be put down, roughly measuring distances - between the camera and subject, patterns in carpets, between doorways in a corridor - allows the focus puller to pull much more accurately than if they were doing so without.
I'm sure David will have a much more concise answer than mine!