The Human Eye
Simple Explanation
The eye's cornea and lens together act as a single converging lens, focusing light onto the retina. Common defects — myopia (near-sightedness) and hyperopia (far-sightedness) — happen when the eye's natural focusing power is slightly wrong, corrected with an external lens of power P=1/f.
Why Do We Need It?
Understanding the eye as an optical instrument explains exactly why corrective lenses (glasses or contacts) work, and connects biology directly to the same lens equation used for cameras and telescopes.
See It
An object on the left with two light rays passing through the eye's lens, converging on the right to form an inverted image on the retina
Formula
Power of a Corrective Lens
P = 1/f
A corrective lens's power (in diopters) is the reciprocal of its focal length — for a myopic (near-sighted) eye, a diverging lens with a focal length equal to the eye's far point brings distant objects into focus.
- P
- — power of the lens, in diopters (D)
- f
- — focal length needed, in metres (m) — negative for a diverging (myopia-correcting) lens
When to use it: Whenever the power of a corrective lens needs to be found from an eye's near or far point.
Worked Example
Find the power of a corrective lens for myopia
A myopic (near-sighted) person's far point is 2 m — the farthest distance they can see clearly, instead of infinity. Find the power of the corrective lens needed.
Why Does This Work?
A myopic eye focuses light from infinity in FRONT of the retina (too much focusing power). A diverging lens spreads incoming light out slightly before it reaches the eye, effectively making a distant object behave — for the eye's own lens — like a closer one that the eye can already focus correctly.
Real-Life Example
Why reading glasses have the opposite curve from myopia glasses
Reading glasses (for hyperopia or age-related presbyopia) use converging lenses, while myopia glasses use diverging lenses.
Hyperopia is the OPPOSITE problem — too little focusing power — so it needs a converging lens to add power, while myopia needs a diverging lens to subtract power; the sign of P in this formula reflects that difference.
Practice
A myopic person's far point is 4 m. Find the power of the corrective lens needed.
MediumCommon mistake
Mixing up which sign of lens corrects which defect — myopia (seeing distant objects poorly) needs a NEGATIVE (diverging) lens power, while hyperopia (seeing near objects poorly) needs a POSITIVE (converging) lens power.
Quick Review
- P = 1/f, in diopters.
- Myopia: diverging lens (negative P). Hyperopia: converging lens (positive P).
- The eye's cornea and lens act together as a single converging lens onto the retina.