According to the Wikipedia article on eye accomodation, the range in which a human eye can focus is from 7 centimetres away up to essentially an infinite distance. Of course, people can't see things an infinite distance away, but at a certain point the light reflected off an object will come at the eye in effectively parallel paths.
As an eye focuses on objects progressively farther away, it seems to me there would be a point when the lens hits maximum flatness, after which it everything will be equally sharp in focus. Looking at an object 500 metres away or 1000 metres away probably doesn't require any change in the lens. However, going from one metre away to seven requires the ciliary muscles adjust to just the right amount.
My question is, what is a normal minimum distance from the eye at which the lens will reach maximum flatness? Everything else in this question is just for context, so an answer to this, stated in metres from the eye, is all I am seeking.
The article I linked to above mentioned the human eye seeing "13 dioptres", and I have tried to understand dioptres, but it's a little confusing for me. If I understand correctly, the higher the dioptre, the closer you focus, so the 13 dioptres refers to how close the human eye can see. If I have this backwards, please let me know.
In any case, my purpose in asking is to determine the range in which ciliary muscles would be required to do more nuanced work in order to hold the lens at in the right shape. Focusing on something 7 centimetres away, the ciliary muscles are at maximum exertion, and at a certain point and beyond the ciliary muscles are completely relaxed. To hold somewhere in between would require more subtly nuanced, and, I suspect, more difficult work on the part of the ciliary muscles.
At least, I assume that to be the case because I am hypothesizing that the act of contraction for the ciliary muscles would be similar to other muscles. For example, it is easier to do a bicep curl with weight when going from full resting position to maximum contraction, as opposed to stopping at a particular spot somewhere in the middle of the motion. To stop mid-motion requires more muscle control, and, depending on how fast you wanted to do it, can be difficult to be exact.
Answer
There are practical questions in ophthalmology and you've asked someone that has a common theoretical answer: 6 meters.
However, you should know that from the same theoretical point the far the object the less accommodation we need, so the second answer is - infinity.
What is the difference? From the practical point the accommodation between this two points is negligible and does not have to be taken into account when we correct the refraction error.
Small theory - to see an object placed at a distance of 1 meter we need 1D of accommodation power (1/1meter=1D), to see an object placed at a distance of 30cm we need 3D of accommodation power (1/0.3meter=3D), for an object at a distance of 10cm we need 10 diopters and finally for an object at the distance of a 6 meter we need accommodate 0.16 diopter.
Thus between 6 meter and infinity the accommodation is very low and this is why the distant visual acuity is checked at this distance. Consequently, the lens convexity difference between 6 meters gaze and infinity is negligible and this is why the answer to your question is between 6 meters and infinity (zero accommodation).
From this explanation you can calculate the dioptric add for any reading distance and understand how the reading spectacles correct the loss of accommodative power (=presbyopia, the vision of older people).
If you want to know how much the crystalline lens changes its dimensions during accommodation, the answer is near 7% for diameter and near 10% for thickness, so the lens as was convex, stays convex and the visible changes are minimal.
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