Span Before Polish: The Dioptric Range a Variable-Focus Spectacle Must Cover, and Why Its Resolution Is Not the Problem

Variable-focus spectacles, in which the wearer dials a power rather than wearing a fixed lens, are repeatedly proposed for settings without refractionists. Their feasibility turns on a number rarely stated: the span of powers one mechanism must cover. For a stated population model of spherical equivalent (mean -0.50 D, standard deviation 2.00 D), covering the central 95 percent of wearers requires a span of 7.84 D, from -4.42 to 3.42 D; the central 99 percent requires 10.3 D. For an Alvarez-type mechanism at a stated sensitivity of 0.35 mm of lateral shift per dioptre, the 95 percent span needs 2.74 mm of travel, and a 0.05 mm setting error costs 0.14 D - inside dispensing tolerance, so resolution is not the obstacle; span, and the cylinder the mechanism cannot correct, are. A buildable specification follows: span at least the 95 percent range, detents every quarter dioptre, and a referral rule for the tails and for astigmats. This study is simulated, not measured.