How the eye works

The human eye is a remarkable natural optical system. Light enters through the cornea and the lens — a biological converging lens — and forms an image on the retina, a layer of light-sensitive cells that transmits the signal to the brain via the optic nerve. It is, in essence, a camera with a single lens and a screen placed at a fixed distance.

That fixed distance between lens and screen poses a problem which the eye solves elegantly.

Principle — Accommodation

In the eye the distance $q$ between the lens and the retina is fixed ($q \approx 2$ cm). To focus on objects at different distances $p$, the lens must change its own focal length $f$, thanks to the small ciliary muscles that deform it. This is the phenomenon of accommodation.

In a camera, focusing is achieved by moving the lens relative to the sensor; in the eye, instead, $q$ is kept constant while $f$ is varied. When this mechanism does not work perfectly, visual defects arise.

Short-sightedness, long-sightedness and glasses

In a “normal” eye, with relaxed muscles, the image of a very distant object forms exactly on the retina. In short-sightedness (myopia) the eye is slightly “too long”: the image of distant objects falls in front of the retina. It is corrected with a diverging lens ($f < 0$) that spreads the rays before they enter the eye, pushing the image back. In long-sightedness (hypermetropia) the eye is “too short” for nearby objects: the lens cannot curve enough to bring them into focus. A converging lens ($f > 0$) is then used to aid accommodation. The dioptres prescribed by the optician are exactly the value $\mathcal{D} = 1/f$ of the corrective lens, positive for the long-sighted and negative for the short-sighted. A $-2$ D pair of glasses means a diverging lens with $f = -50$ cm.

Collegamenti

Argomenti: Ottica Concetti: Lenti e specchi

Esercizi collegati: Problema — Raggi per oggetto oltre 2f (lente) · Problema — Raggi per specchio concavo con p minore di f · Esercizio svolto — Specchio concavo