The Optical Model of the Eye
Myopia, hyperopia and the mathematics of glasses
Summary
The eye is a biological camera: the cornea and the lens bend light and focus it on the retina. If the focus falls in front of the retina, the eye is myopic (short-sighted: distant things look blurry); if it falls behind, it is hyperopic (long-sighted: near things look blurry). Glasses of the right dioptre correct this error.
In depth
The human eye is about 24 mm long on average: small, but an optically remarkable device. Light enters first through the cornea (where most of the bending happens), and is then fine-tuned by the lens, whose shape is changed by the ciliary muscles (accommodation). In a healthy eye, parallel rays from far away meet on the retina; for near objects the lens thickens and keeps the focus short. In myopia the eye is too long or the lens too strong, so rays from far away focus in front of the retina and distant objects look blurry. In hyperopia the eye is too short or the lens too weak, so the focus falls behind the retina and near objects look blurry. Glasses fill the gap: for myopia a concave lens (negative dioptres) spreads the rays out so the eye's focusing power is reduced; for hyperopia a convex lens (positive dioptres) gathers the rays and adds the power the eye lacks.
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