The Human Eye and Vision Correction

The human eye focuses light from objects onto the retina using the cornea and an adjustable lens, forming a real, inverted image that the brain interprets as upright; common refractive defects are myopia (short-sightedness), corrected by a concave lens, and hyperopia (long-sightedness), corrected by a convex lens. In brief: the eye has a total optical power of about 60 dioptres, of which about two-thirds comes from the cornea. Accommodation is the change in the shape (and power) of the lens by the ciliary muscles to focus on near objects. The normal near point is about 25 cm, and the far point is at infinity.

About half of the people in some countries need glasses or contact lenses. This guide describes the parts of the eye and how images are formed, explains accommodation and the common defects of vision, compares the defects and their corrections in a table, works through lens power calculations for glasses and corrects common mistakes.

How does the eye form an image?

Light enters through the transparent cornea, which does most of the refraction (about 43 dioptres). It then passes through the pupil, the opening in the colored iris, whose diameter is controlled to adjust the amount of light (about 2 to 8 mm). The lens (about 15 to 20 D, adjustable) fine-tunes the focus. The image falls on the retina, the layer of light-sensitive cells: about 120 million rods (sensitive to dim light, no color) and 6 million cones (color vision and detail, concentrated in the fovea). The optic nerve carries signals to the brain. The eye is filled with the transparent aqueous humor in front and the vitreous humor behind the lens. The distance from the lens to the retina is about 2.4 cm and fixed, so, to focus objects at different distances, the focal length of the lens must change.

What is accommodation?

For distant objects, the ciliary muscles relax, and the lens is thin (longer focal length). For near objects, the ciliary muscles contract and the lens becomes thicker (shorter focal length, higher power). The nearest point at which an object can be seen clearly is the near point (about 25 cm for a young adult; it gets farther with age because the lens becomes stiffer, a condition called presbyopia, which needs reading glasses). The farthest point of clear vision is the far point, which is at infinity for a normal eye.

What are the common defects of vision?

• Myopia (short-sightedness): distant objects are blurred. The eyeball is too long or the lens too powerful, so the image of distant objects forms in front of the retina. The far point is closer than infinity. Correction: a concave (diverging) lens, which makes the rays diverge slightly before they enter the eye.
• Hyperopia (long-sightedness): near objects are blurred. The eyeball is too short or the lens too weak, so the image of near objects would form behind the retina. The near point is farther than 25 cm. Correction: a convex (converging) lens.
• Astigmatism: the cornea is not spherical, so lines in some directions are blurred. Correction: a cylindrical lens.
• Presbyopia: loss of accommodation with age. Correction: reading glasses, bifocals or progressive lenses.
• Cataracts (clouding of the lens) and other diseases are treated by surgery; laser surgery can reshape the cornea.

Defects and corrections compared

Worked example: prescription lenses

1. Myopia. A person’s far point is 50 cm, and they need to see distant objects clearly. The glasses must form a virtual image of a distant object (d_o = ∞) at the far point, 0.50 m in front of the eye. So d_i = −0.50 m and 1/f = 1/∞ + 1/(−0.50) = −2.0 m⁻¹, so f = −0.50 m and P = −2.0 D. (The distance between the glasses and the eye is neglected.) A concave lens.
2. Hyperopia. A person has a near point of 100 cm, and wants to read at the normal distance of 25 cm. The lens must form a virtual image at 1.00 m of an object at 0.25 m: 1/f = 1/0.25 + 1/(−1.00) = 4.0 − 1.0 = 3.0 D. So P = +3.0 D (f = 33 cm). A convex lens.
3. Accommodation needed. The distance from the lens system to the retina is fixed. A relaxed normal eye forms the image of a distant object (d_o = ∞) on the retina. To see an object at the near point of 25 cm on the same retina, the power of the eye must increase by 1 ÷ d_o = 1 ÷ 0.25 m = 4.0 D (from 1/f = 1/d_o + 1/d_i with d_i fixed). A young person can accommodate by 10 D or more, which is why they can see objects as close as 10 cm; by the age of 50 the range falls to about 2 D, and reading glasses are needed.
4. Size of the retinal image. A person 1.8 m tall seen from 20 m: the angle is about 1.8 ÷ 20 = 0.09 rad. The image height with the nodal distance of 17 mm is 0.09 × 17 = 1.5 mm.

How was vision understood?

Ibn al-Haytham showed in the 11th century that vision results from light entering the eye, not leaving it. Eyeglasses for presbyopia appeared in Italy around 1286, and concave lenses for myopia in the 15th century. Johannes Kepler explained in 1604 that the lens forms an inverted image on the retina and that defects result from the focus falling in the wrong place. Thomas Young described accommodation and astigmatism in 1801. Contact lenses were developed in the 19th and 20th centuries, and laser vision correction (LASIK) became widespread in the 1990s.

Which mistakes are common?

Mistake 1: Mixing up myopia and hyperopia

Myopia = near-sighted (distant things blurred), corrected by concave lenses. Hyperopia = far-sighted (near things blurred), corrected by convex lenses.

Mistake 2: Saying that the retina receives an upright image

The image on the retina is inverted. The brain interprets it.

Mistake 3: Saying that the lens does all the focusing

The cornea provides about two-thirds of the power. The lens adjusts the focus.

Mistake 4: Forgetting the sign of the power

Negative dioptres are for concave lenses (myopia) and positive for convex lenses.