The eye as an optical system

One converging system, one fixed screen

Light entering the eye is bent twice. Most of the bending happens at the cornea, the curved front window, because that is where light crosses the largest change of refractive index. The lens behind it makes the smaller adjustment, and the iris opens and closes the pupil to control how much light gets in. For calculations the whole arrangement is treated as one thin converging lens, with the retina acting as the screen about 23 mm behind it.

So the image on the retina is real, inverted and diminished. Nothing later turns it the right way up. The brain learns to interpret it, so a question about the retinal image is a question about the optics, not about perception.

Three equations from the lenses lesson do all the arithmetic here. Power and focal length are two names for one property,

with f in metres and P in dioptres. Object distance, image distance and focal length are tied together by

in the real-is-positive convention, and the size of the image follows from

Accommodation: the power that changes

The retina cannot move, so v is stuck at about 23 mm whatever you look at. Read 1/u + 1/v = 1/f with v fixed and one thing has to give. When u changes, f must change with it, and the eye must supply a different power for every distance. The ciliary muscles do it indirectly: contracting, they slacken the suspensory ligaments holding the lens, and the elastic lens rounds itself into a fatter, more strongly converging shape. That is accommodation.

Two distances mark the limits of what accommodation can reach. The far point is the furthest object the eye can focus, at infinity for a healthy eye, and the eye is fully relaxed there. The near point is the closest, taken as 0.25 m for a normal adult eye and reached with the lens working hardest. That 0.25 m is also called the least distance of distinct vision, and it is the distance every reading calculation assumes.

Accommodation has limits, and the near point and the far point are where they show. When the far point comes in from infinity, or the near point moves out beyond 0.25 m, the eye has a defect of vision that a spectacle lens corrects.

The retina as a photodetector

As a detector the eye has two kinds of cell. Cones work in bright light, come in three types responding to different bands of wavelength, and between them give colour vision. Rods work in dim light, come in one type only, and so report brightness and nothing about colour.

That figure is the eye's spectral response, and it is the reason the visible spectrum ends where it does. Sensitivity peaks in the yellow-green, near 555 nm in good light, and falls to nothing outside roughly 400 nm to 700 nm. The rods peak at a shorter wavelength, near 500 nm, so as the light fades the eye's peak sensitivity shifts towards blue-green and reds go dark first. That is a shift in sensitivity, not a new best colour, because the rods that take over do not distinguish colours at all.

Spatial resolution depends on how closely the cells are packed and how they are wired. Cones crowd into the fovea, a small patch on the axis of the eye, and each one there has effectively its own nerve fibre. Two lit cones with an unlit one between them therefore arrive at the brain as two separate signals, and detail survives. Rods lie outside the fovea and many of them share a single fibre, so their signals are added together before they leave the eye.

That convergence increases sensitivity in low light but reduces spatial resolution, because the brain cannot tell which rod in the group was lit; it is why the dark-adapted eye can work by starlight. Cones have less convergence, giving greater acuity in bright light, and the eye's practical resolution of about one minute of arc, roughly 3 × 10⁻⁴ rad, is a fovea figure. Look slightly to one side of a faint star and it brightens, because you have moved its image off the fovea and onto the rods.