The Eye and Corrective Lenses - Physics for Pilot Assessments

The eye is a converging lens with a screen behind it, and every rule from the previous lesson applies to it unchanged. That is the whole of this lesson's claim, and the reason it is worth a lesson of its own is that the two commonest defects of vision, and the two lenses that correct them, are pure ray geometry — you can work out which lens fixes which defect from first principles rather than remembering it, and the items in this area are built on the assumption that you will not.

What in the eye does the focusing

Light entering the eye is bent twice, not once. The first and larger bend happens at the cornea, the curved transparent layer at the very front, where light crosses from air into the much denser tissue behind it — and because that is the boundary with the biggest change of refractive index anywhere in the eye, the cornea does roughly two thirds of the total bending. Behind it sits the pupil, the adjustable hole through which light passes, whose diameter is set by the coloured ring of muscle around it called the iris. The pupil controls how much light gets in; it does no focusing at all.

Behind the pupil is the lens proper: a flexible, slightly yellowish converging lens which supplies the remaining third of the bending and, crucially, is the part whose shape can be changed. Light passing through it crosses the jelly filling the eyeball and lands on the retina, the light-sensitive layer lining the inside of the back wall. The retina is the screen, and because a real image is the only kind that shows up on a screen, the image formed on it is real — which means, by the pairing established in the last lesson, that it is also inverted. The image on the back of your eye is upside down, and your brain simply learns to interpret it that way round.

In the language of the last lesson, then, ordinary vision is the object-beyond-2F case: object far away, image real, inverted and much smaller, formed just outside the focal point. The eye's focal length is only about 2 centimetres because the retina is only about that far behind the lens, which makes the eye as a whole a lens of roughly 50 dioptres — one divided by 0.02 metres — and a very powerful one by everyday standards.

Accommodation: focusing near and far

There is a difficulty built into that arrangement. The distance from the lens to the retina is fixed by the size of your eyeball, so v cannot change. But the thin lens equation ties f, u and v together, so if u changes when you look from a distant hill to a book in your hands and v cannot move, then f must change instead. It does. A ring of muscle around the lens squeezes it into a fatter, more strongly curved shape, which shortens its focal length and increases its power, and that is what brings a near object into focus on an unmoved retina. Relax the muscle and the lens flattens, the focal length lengthens, and distant objects come into focus. This adjustment is called accommodation.

Two consequences are worth noting because they connect to the defects below. Focusing on something close is the active, muscular state, which is why prolonged close work tires the eyes and why relaxing your gaze into the distance rests them. And the lens stiffens with age, so the range over which it can be reshaped narrows; the near limit drifts outwards from a few centimetres in childhood to well beyond arm's length in later life. That gradual loss of accommodation is a different thing from the two defects that follow, which are about the eye's overall focusing power being mismatched to its length rather than about the adjustment failing.

Panel 1: a normal eye, where parallel rays from a distant object are brought together exactly on the retina. Panel 2: short sight, where they meet in front of the retina and are already spreading again by the time they land — a diverging lens in front of the eye spreads them first, so the eye's own convergence takes longer to act and the meeting point moves back. Panel 3: long sight, where they are still converging when they reach the retina and would meet behind it — a converging lens bends them inward first, so the meeting point moves forward.

Short sight

Short sight, or myopia, is the condition in which distant objects look blurred while near ones are sharp. Geometrically it means the eye is bending light too strongly for its own length: either the cornea and lens are too powerful, or the eyeball is a little too long from front to back, and the result is the same. The rays from a distant object are brought together at a point in front of the retina, and by the time they reach the retina they have crossed and started spreading again, so each point of the object is smeared into a small disc rather than landing as a point. That smearing is what blurred means.

The correction has to move the meeting point backwards, which means the light must arrive at the eye less strongly converged than it would otherwise be — so you put a diverging lens in front of it. A diverging lens spreads rays apart, and spread-out rays take the eye's fixed converging power longer to bring together, which pushes the focus further back until it lands on the retina. That is the whole argument, and it is worth reconstructing it that way rather than memorising the pairing, because the memorised version is exactly what the distractors are designed to catch. Near objects were already in focus and stay so, because accommodation can still flatten the lens for them.

Long sight

Long sight, or hypermetropia, is the mirror image: near objects look blurred while distant ones are sharp. Here the eye is not bending light strongly enough for its length — the cornea and lens are too weak, or the eyeball is a little too short — so the rays are still converging when they reach the retina and would only have met at a point behind it. Again each point of the object lands as a disc rather than a point, and again the result is blur, but the failure is the opposite one.

The correction must therefore move the meeting point forwards, which means giving the light a head start on converging before it ever reaches the cornea: a converging lens. It bends the rays inward first, adding its power to the eye's, so the combination is strong enough to bring them together a little sooner — on the retina rather than behind it. Because powers add, that is also the sense in which the two corrections are opposites in a single arithmetic: the corrective lens supplies whatever the eye is short of, positive dioptres for long sight and negative for short sight.

Reading a prescription

The number on a spectacle prescription is a power in dioptres, which is one divided by the focal length in metres — the same relationship as in the previous lesson, repeated here because a prescription is the place you are most likely to meet it in an item.

Lens power

P = \frac{1}{f}

$P$: power of the lens, in dioptres (D), where 1 D = 1 per metre
$f$: focal length in metres (m) — positive for converging, negative for diverging

The sign is the diagnosis. A negative power means a diverging lens, which means the wearer is short-sighted; a positive power means a converging lens and long sight. The size of the number says how far from normal the eye is, so a −4 D lens belongs to a more short-sighted eye than a −1 D one. The two examples below run that relationship in each direction, because items ask it both ways.

Example 3 — from the symptom to the lens

Someone finds street signs across the road perfectly sharp, but has to hold a book out at arm's length before the print comes into focus. Which defect is this, which lens corrects it, and what sign will the prescription carry?

Sort the symptom first: distance sharp, near blurred. Blurred near vision with clear distance vision is long sight.
Locate the failure: for a near object this eye is not bending the light strongly enough, so the rays are still converging at the retina and would only meet behind it.
Choose the fix by direction: the meeting point has to move forward, so the light needs extra convergence before it reaches the eye — a converging lens.
A converging lens has positive power, so the prescription carries a plus sign: something like +2 D.
Run the opposite case as a check: a diverging lens would spread the rays and push the meeting point still further back, making the blur worse. Only the converging lens moves the focus the way this eye needs.

Why it matters in aviation

How the eye focuses, and the particular ways it fails to, is why pilot medical standards state vision requirements at distance and at near and allow correction only within limits. Accommodation is the reason the two have to be assessed separately: the lens stiffens with age, so the near limit drifts outwards while distance vision may be untouched, and a crew member can end up needing one correction for reading the panel and charts and a different one, or none, for scanning outside.

The retina accounts for the other half of the job. Cones, concentrated at the centre of the retina, give colour and fine detail but need a reasonable amount of light; rods, spread across the periphery, are the sensitive ones in darkness and report no colour. At night the centre of the field is therefore the weakest part of it, so staring straight at a faint light or a distant aircraft can lose it altogether. Scanning in short steps, and looking slightly to one side of whatever you are trying to make out, puts the image on the sensitive periphery instead, and that is the standard technique for looking out in the dark.

What the test asks

One trap dominates, and it is simply the two corrections swapped: a converging lens offered for short sight, or a diverging one for long sight. Do not try to hold the pairing in memory, because the two words sound interchangeable under time pressure — rebuild it in one step from the last lesson instead. A diverging lens spreads rays, spread rays take longer to converge, so the focus moves further back, so it fixes a focus that was falling short: short sight. Everything else follows by opposition. Secondary distractors put the image on the retina the right way up, when a real image is always inverted; credit accommodation to the pupil or the iris rather than to the lens changing shape, when the pupil only controls brightness; and describe short sight as the eye being too weak, when it is the eye being too strong for its length.