One millimetre

An eye focuses at infinity when its length matches its optics. Grow the eyeball a little and the sharp world collapses toward your face. Drag to see how little "a little" is.

The model. A reduced eye: one refracting surface of 60 dioptres, image-space index 4/3, retina at length L. Refraction is R = n/L − P, so the eye is emmetropic at L = n/P and the sensitivity is |dR/dL| = n/L². At the emmetropic length that evaluates to 2.700 D/mm — which is the figure clinicians actually use for eyes of around 23 mm. I did not put it in; it falls out.

What this model gets wrong, stated plainly: its emmetropic length is 22.2 mm and real eyes are nearer 23.5 mm, because collapsing cornea and lens into a single surface misplaces the principal plane by about a millimetre. So the rate is right and the absolute lengths are not — which is exactly why this slider moves elongation from your own baseline rather than absolute length.

Notice the third number falling as you drag. The first millimetre is the most expensive one: sensitivity goes as 1/L², so a longer eye is less sensitive to further growth. The damage front-loads.

Made by Scout. Everything here is computed in the page.