The optics of the eye: power, accommodation and correction
The eye as a converging lens system, power in dioptres, accommodation and the near point, retinal image size, correcting myopia and hyperopia, photoreceptor spectra and the X-linked inheritance of colour vision deficiency. With a near-point and accommodation investigation.
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The eye is a converging optical system. The cornea provides about two-thirds of its power, because light slows a lot on entering it from air (n = 1.38 for the cornea); the lens (average n = 1.41) provides the rest. The eye forms a real, inverted image on the retina, which the brain interprets the right way up.[4]
Lens power is P = 1/f, in dioptres (1 D = 1 m⁻¹). The thin-lens equation is P = 1/d_o + 1/d_i. With a lens-to-retina distance d_i = 2.00 cm, the relaxed eye has P = 50.0 D for distant objects. To focus at the near point of 25 cm, the ciliary muscle makes the lens thicker and P rises to about 54.0 D: this is accommodation. The near point moves further away with age.[4]
Magnification is m = h_i/h_o = −d_i/d_o. A hair 1.20 × 10⁻² cm wide seen from 60.0 cm forms an image only 4.00 × 10⁻⁴ cm wide on the retina.[4]
A myopic eye over-converges: its eyeball is too long, rays from distant objects cross in front of the retina and the far point is closer than infinity. It is corrected with a diverging lens of negative power: for a far point of 30.0 cm and glasses 1.50 cm from the eye, P = 1/∞ + 1/(−0.285 m) ≈ −3.51 D. A hyperopic eye (eyeball too short) is corrected with a converging lens of positive power. Laser surgery reshapes the cornea instead.[5][6][2]
Rods contain rhodopsin, which absorbs best at about 498 nm, and work in dim light. Three cone opsins absorb best at about 420, 534 and 564 nm; colour is the brain's comparison of their activity. In the fovea each cone connects to a single ganglion cell, giving the sharpest vision; in the periphery up to 50 receptors converge on one. The ganglion cell axons form the optic nerve, and where it leaves the retina is the blind spot.[3]
Visible light runs from about 380 to 740 nm, and humans can distinguish about 2 million colours. Thanks to the pupil and chemical adaptation, the eye works over light intensities spanning a factor of about 10¹⁰.[2][4]
Red-green colour vision deficiency, the most common type, is inherited. The gene is on the X chromosome: males (XY) need only one copy, while females (XX) would need it on both, which is rare.[7]
Try it: Measure your near point and accommodation
You need
- A card with small printed text
- A metre rule
- A partner
- Results table
- Calculator
- Optional: a converging lens from the lab kit and a white screen
Safety
Never point the rule or the card corner at an eye; measure to the cheekbone. Never look at the Sun or a lamp through a lens, and don't focus sunlight with the lens. Stop if your eyes feel strained. This is a physics activity, not an eye test.
What to do
- Wear your usual glasses or contact lenses, if you have them, and note this in the table.
- Cover one eye. Hold the card at arm's length and slowly bring it towards your open eye until the text just starts to blur. Stop there.
- Your partner measures the distance from the card to the edge of your eye socket (cheekbone) with the metre rule. Repeat 3 times; then test the other eye.
- Calculate the mean near point d_np (in m) and the uncertainty (half the range) for each eye.
- Accommodation is the extra power the eye adds: P_near − P_far = (1/d_np + 1/d_i) − (1/∞ + 1/d_i) = 1/d_np. Calculate it in dioptres and compare with the textbook eye (54.0 D − 50.0 D = 4.0 D for a near point of 25 cm).
- Optional: focus a distant window onto the white screen with the lab lens, measure f and calculate its power P = 1/f.
What happens, and why?
To focus on a close object, the ciliary muscle makes the lens thicker and more converging, raising the eye's power. The closest distance at which you can still focus is your near point, so 1/d_np is the most extra power your eye can add. The textbook standard is 25 cm (4.0 D), and the near point moves further away with age as the lens becomes less flexible.[4][6]
Play: Myopia or hyperopia?
Each card describes an eye or a correction. Is it about myopia (nearsightedness) or hyperopia (farsightedness)?
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Quiz
Other ages: Ages 6–7 · Ages 10–11