Teacher sheet · Ages 15–16 · about 45–50 minutes
The optics of the eye: power, accommodation and correction
Lesson page: echoesof.science/school/eyes/ages-15-16/ · Pupil worksheet: echoesof.science/school/eyes/ages-15-16/print/
Learning aims
- Model the eye as a converging lens system and use P = 1/f and P = 1/d_o + 1/d_i.
- Explain accommodation and the near point, and calculate accommodation in dioptres.
- Explain and calculate the correction of myopia and hyperopia.
- Describe rod and cone spectra, foveal wiring and X-linked colour vision deficiency.
- Measure and evaluate data with uncertainties.
Lesson plan
| Time | Activity |
|---|---|
| 5 min | Starter: why does a magnifying glass make things look bigger, and what does the eye have in common with it? |
| 10 min | Read the text; work through the 50 D and 54 D examples. |
| 20 min | Near-point and accommodation investigation. |
| 5 min | Calculations: accommodation, myopia correction, retinal image size. |
| 5 min | Quiz or the myopia game. |
Materials for the experiment
- 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.
Common misconceptions
| Pupils may think… | Actually… |
|---|---|
| The lens does almost all the focusing. | The cornea provides about two-thirds of the power. |
| Nearsighted people can't see near things. | They see near things clearly; distant things blur. |
| The image on the retina is the right way up. | It is real and inverted; the brain interprets it. |
Worksheet answers
- P = 1/0.50 m + 1/0.0200 m = 2.0 D + 50.0 D = 52.0 D.
- Light slows considerably going from air into the cornea (n = 1.38); inside the eye the lens (n ≈ 1.41) sits between fluids of n = 1.34, so its refraction is smaller.
- Answers depend on data; for a near point of 0.20 m, accommodation = 1/0.20 = 5.0 D, compared with 4.0 D for the textbook 25 cm.
- The eye over-converges, so distant rays must be diverged first; the lens must make an image of a distant object at the far point, 28.5 cm from the glasses: P = 1/∞ + 1/(−0.285 m) ≈ −3.51 D.
Quiz answers
- A relaxed eye with d_i = 2.00 cm views a distant object. Its power is… 50.0 D. P = 1/∞ + 1/0.0200 m = 50.0 D.[4]
- Focusing on an object at 25.0 cm needs how much extra power? 4.0 D. 1/0.25 m = 4.0 D (54.0 D − 50.0 D).[4]
- Which part of the eye provides about two-thirds of its focusing power? The cornea. Light slows most on entering the cornea from air.[4]
- Which lens corrects myopia? A diverging lens with negative power. For a far point of 30.0 cm the example gives about −3.51 D.[5]
- In the fovea, each cone connects to… one ganglion cell. One-to-one wiring gives the sharpest vision; in the periphery up to 50 receptors converge.[3]
- Why is red-green colour deficiency more common in males? One X chromosome means one copy of the gene is enough. Females would need the gene on both X chromosomes.[7]
Going further
Use P = 1/d_o + 1/d_i to work out the power of reading glasses for someone whose near point is 1.00 m, so they can read at 25.0 cm with glasses 1.50 cm from the eye. Check against the textbook answer of about +3.24 D.
Sources used in this lesson
- [2] Biology 2e, 36.5 Vision (OpenStax, Rice University): reliability High
- [3] Anatomy and Physiology, 14.1 Sensory Perception (OpenStax, Rice University): reliability High
- [4] College Physics 2e, 26.1 Physics of the Eye (OpenStax, Rice University): reliability High
- [5] College Physics, 26.2 Vision Correction (OpenStax, Rice University): reliability High
- [6] Types of Refractive Errors (National Eye Institute (NIH, USA)): reliability High
- [7] Causes of Color Vision Deficiency (National Eye Institute (NIH, USA)): reliability High
Full list with links and a note on each source's reliability: echoesof.science/school/eyes/sources/
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