Read

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.

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.

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.

Experiment: Measure your near point and accommodation

1. Wear your usual glasses or contact lenses, if you have them, and note this in the table.
2. 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.
3. 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.
4. Calculate the mean near point d_np (in m) and the uncertainty (half the range) for each eye.
5. 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).
6. Optional: focus a distant window onto the white screen with the lab lens, measure f and calculate its power P = 1/f.

Eye	Run 1 (cm)	Run 2 (cm)	Run 3 (cm)	Mean d_np (m)	1/d_np (D)
Right eye
Left eye

Questions

1. Use P = 1/d_o + 1/d_i (d_i = 2.00 cm) to calculate the eye's power for an object at 50 cm.

2. Explain why the cornea contributes more power than the lens.

3. Give your near point and accommodation (in D) with uncertainties and compare with the textbook eye.

4. A person's far point is 30.0 cm. Explain why they need a lens of negative power, and calculate it for glasses worn 1.50 cm from the eye.

Sources for every fact on this sheet: echoesof.science/school/eyes/sources/

🖨 Print this sheet ← back to the lesson