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Physics of the Eye: How We See and How Lenses Fix Vision

The eye is a converging lens system: the cornea does most of the bending and the lens fine-tunes the focus (accommodation). Light lands on the retina, where rods give sensitive night vision with poor detail and three types of cones give colour and fine detail. A normal eye has a near point of about 25 cm and a far point at infinity. Myopia (eye too long) is corrected with a diverging lens of f = βˆ’far point; hypermetropia (eye too short) with a converging lens; astigmatism with a cylindrical lens. Lens power P = 1/f in dioptres (D), and powers of thin lenses in contact add.

🎬 Step-by-step story

  1. Rays from a far object arrive parallel. The cornea and lens bend them so they meet exactly on the retina. Sharp picture!
  2. Zoom into the retina: grey rods for dim light, and three kinds of cones (blue, green, red) for colour and detail.
  3. Now bring the object near. Its rays spread out. The lens gets fatter (accommodation) so the focus lands on the retina again.
  4. Short sight: the eyeball is too long, so far rays meet in front of the retina. A diverging (βˆ’) lens moves the focus back.
  5. Long sight: the eyeball is too short, so near rays would meet behind the retina. A converging (+) lens brings them forward.
  6. Free play: switch the eye type, move the object and put glasses on. Find the sharp focus each time.

Tip: drag the 3D scene to turn it. Use two fingers to zoom.

πŸ€” Common doubts, cleared

If the lens can change shape, why does the cornea do most of the bending?

Bending depends on the change in refractive index. Air to cornea is a big jump (1.00 to about 1.38). Inside the eye the lens is surrounded by fluids with similar index, so its bending is smaller.

Why can't I see colours in very dim light?

Only rods work in dim light, and there is only one type of rod, so the brain has nothing to compare. Colour needs the three cone types, which need brighter light.

Why does the lens get fatter for near objects, not thinner?

Rays from a near object are spreading out, so the eye needs more converging power. A fatter lens is more curved, so it has more power.

Why does a short-sighted person need a diverging lens when the eye is already a converging lens?

The eye is too strong for its length. The diverging lens takes away a little power, so far rays meet further back, on the retina.

How does a converging lens help long sight?

It adds power so rays from a book at 25 cm can be focused. It makes a virtual image of the book at the person's own near point, where they can see it.

Is the image on the retina upside down?

Yes, it is real and inverted, like in a camera. The brain flips it so we see the world upright.

The eye as an optical system

The eye works like a camera with a converging lens. Light passes through the cornea (clear front window), the aqueous humour, the pupil (hole in the iris that controls how much light enters), the lens and the jelly-like vitreous humour, then lands on the retina.

Most of the bending (about +40 D of the total +60 D) happens at the cornea, because the jump from air to cornea is the biggest change in refractive index. The lens adds the rest and can change its shape.

Ray diagrams and the lens equation

We model the eye as one thin converging lens. With the real-is-positive rule: 1/f = 1/u + 1/v and P = 1/f (dioptres, f in metres). The image on the retina is real, inverted and smaller; the brain turns it the right way up.

Accommodation, near point and far point

Accommodation is the eye changing its power to focus at different distances. When the ciliary muscles relax, the suspensory ligaments pull the lens thin: low power, good for far objects. When they contract, the lens gets fatter: more power, good for near objects.

The far point is the furthest point you see clearly (infinity for a normal eye). The near point is the closest (about 25 cm for a young adult). It moves further away with age (presbyopia), because the lens gets stiffer.

Sensitivity, colour and spatial resolution

The retina has two kinds of light detector:

Why rods give poor detail

Many rods share one nerve fibre, so the brain cannot tell which rod was hit. Each fovea cone has its own fibre. Two points look separate only if their images fall on two cones with at least one unstimulated cone between them. This gives a best resolution of roughly 1 arc-minute (about 3 Γ— 10⁻⁴ rad).

Persistence of vision

An image stays for about 1/10 s, so frames shown faster than about 20 per second blend into smooth motion.

Defects of vision and their correction

Myopia (short sight)

Far point is closer than infinity. Rays from far objects focus in front of the retina. Fix: a diverging lens that makes far objects seem to be at the far point. f = βˆ’(far point distance).

Hypermetropia (long sight)

Near point is further than 25 cm. Fix: a converging lens that takes an object at 25 cm and forms a virtual image at the person's near point. Use 1/f = 1/u + 1/v with u = +0.25 m and v = βˆ’(near point).

Astigmatism

The cornea is curved more in one direction than another, so lines in one direction are blurred. Fix: a cylindrical lens with its axis set at the right angle. A prescription gives power and axis angle.

Combining lenses

Thin lenses in contact: P = P₁ + Pβ‚‚.

Try it

Hold a pencil at arm's length and bring it slowly towards one eye. Note where it first goes blurry: that is your near point. Cover one eye and look at a printed word in a dark room as your eyes adjust β€” you lose colour first. In the 3D, choose short sight, then press glasses and watch the focus move back onto the retina.

Key formulas and definitions

Worked examples

1. A lens has focal length 25 cm. What is its power?

P = 1/f = 1/0.25 = +4 D.

2. A short-sighted person has a far point of 2.0 m. Find the power of the correcting lens.

The lens must make objects at infinity appear at 2.0 m, so f = βˆ’2.0 m. P = 1/(βˆ’2.0) = βˆ’0.5 D (diverging).

3. A long-sighted person's near point is 1.0 m. What lens lets them read at 25 cm?

u = 0.25 m, v = βˆ’1.0 m (virtual image). 1/f = 1/0.25 + 1/(βˆ’1.0) = 4 βˆ’ 1 = 3. P = +3 D, f β‰ˆ 0.33 m (converging).

4. A myopic eye's far point is 50 cm. With the correct lens, what is the new near point if the bare near point was 15 cm?

Lens: f = βˆ’0.50 m. Object at u gives virtual image at v = βˆ’0.15 m: 1/u = 1/f βˆ’ 1/v = βˆ’2 + 6.67 = 4.67, so u β‰ˆ 0.21 m. New near point β‰ˆ 21 cm.

5. Two thin lenses of +2.5 D and βˆ’1.0 D touch. Find the combined focal length.

P = 2.5 βˆ’ 1.0 = +1.5 D. f = 1/1.5 β‰ˆ 0.67 m.

6. Estimate the smallest gap between two dots you can resolve at 25 cm if the eye resolves 3 Γ— 10⁻⁴ rad.

Gap = angle Γ— distance = 3 Γ— 10⁻⁴ Γ— 0.25 β‰ˆ 7.5 Γ— 10⁻⁡ m β‰ˆ 0.08 mm.

Common mistakes

Practice quiz

1. Where does most of the eye's refraction happen?
2. Which cells give colour vision?
3. Myopia is corrected with a:
4. A lens of power βˆ’4 D has focal length:
5. Why is detail poor in rod vision?

Practice: answer these yourself

Type or choose your answer, then press Check. Use a hint if you are stuck; the full solution appears after you answer.

Frequently asked questions

How do you calculate the power of a lens to correct myopia?

Take the far point in metres and make it negative: f = βˆ’far point. Then P = 1/f. For a far point of 2 m, P = βˆ’0.5 D.

What is the difference between rods and cones?

Rods are very sensitive and work in dim light but give no colour and poor detail. Cones need bright light, come in three types for colour and give fine detail in the fovea.

What lens corrects astigmatism?

A cylindrical lens, which adds power in one direction only, matched to the direction in which the cornea is mis-shaped.

Where this is taught

England (GCSE, A level)Year 133.10 Medical physics

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