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I don't have any physics background aside from intro physics so apologies if my question sounds very shallow.

If lens power is based on focal length, but our eyes adjust its focal length based on the distance of the object we are observing, how do we know that our lens prescription is correct for all distances? Most eye tests I have done involve focusing on objects at a far distance. If our lens prescription is based on focal length when we focus on objects at a far distance, is it incorrect to be using this prescription when doing near distance work?

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An "ideal" eye can adjust its optical system from the near point, $25\,\rm cm$ (least distance of distinct vision) from the eye, to the far point at "infinity" (largest distance of distinct vision).

When things go wrong that range might change and the optical system has to be adjusted by using external lenses.

If the unaided eye has a far point which is less than "infinity" (short sight) then the optical system of the eye can be adjusted by adding a suitable lens diverging which corrects for this.
At the same time this will also increase the least distance of distinct vision but if that is a small change in distance, which it often is, then no correction is necessary.
On the other hand if the correction to short sight results in a large change to viewing objects which are close another correction lens will be needed in the form of another pair of spectacles (reading glasses), bifocal lenses of varifocal lenses.

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