35.3.2 Refractive Errors of the Eye and Their Correction
The near point of normal vision is considered to be 25 cm, but the near point of any individual changes with age. The near point of young children can be as little as 10 cm. The “normal” 25 cm near point is characteristic of young adults, but the near point of most individuals begins to move outward by age 40 or 45 and can reach 200 cm by age 60. This loss of accommodation, which arises because the lens loses flexibility, is called presbyopia. Even if their vision is otherwise normal, individuals with presbyopia need reading glasses to bring their near point back to 25 or 30 cm, a comfortable distance for reading.
Presbyopia is known as a refractive error of the eye. Two other common refractive errors are hyperopia and myopia. All three can be corrected with lenses—either eyeglasses or contact lenses—that assist the eye’s focusing. Corrective lenses are prescribed not by their focal length but by their power, the inverse of the focal length in m.
A person who is farsighted can see faraway objects (but even then must use some accommodation rather than a relaxed eye), but his near point is larger than 25 cm, often much larger, so he cannot focus on nearby objects. The cause of farsightedness—called hyperopia—is an eyeball that is too short for the refractive power of the cornea and lens. As FIGURES 35.9a and b show, no amount of accommodation allows the eye to focus on an object 25 cm away, the normal near point.
FIGURE 35.9 Hyperopia.
With hyperopia, the eye needs assistance to focus the rays from a near object onto the closer-than-normal retina. This assistance is obtained by adding refractive power with the positive (i.e., converging) lens shown in FIGURE 35.9c. To understand why this works, recall that the image of a first lens acts as the object for a second lens. The goal is to allow the person to focus on an object 25 cm away. If a corrective lens forms an upright, virtual image at the person’s actual near point, that virtual image acts as an object for the eye itself and, with maximum accommodation, the eye can focus these rays onto the retina. Presbyopia, the loss of accommodation with age, is corrected in the same way.
The optometrist’s prescription is for the right eye (top) and for the left (bottom), the minus sign indicating that these are diverging lenses. The optometrist doesn’t write the D because the lens maker already knows that prescriptions are in diopters. Most people’s eyes are not exactly the same, so each eye usually gets a different lens.
NOTE Figures 35.9 and 35.10 show the corrective lenses as they are actually shaped—called meniscus lenses—rather than with our usual lens shape. Nonetheless, the lens in Figure 35.9c is a converging lens because it’s thicker in the center than at the edges. The lens in Figure 35.10c is a diverging lens because it’s thicker at the edges than in the center.
A person who is nearsighted can clearly see nearby objects when the eye is relaxed (and extremely close objects by using accommodation), but no amount of relaxation allows her to see distant objects. Nearsightedness—called myopia—is caused by an eyeball that is too long. As FIGURE 35.10a shows, rays from a distant object come to a focus in front of the retina and have begun to diverge by the time they reach the retina. The eye’s far point, shown in FIGURE 35.10b, is less than infinity.
FIGURE 35.10 Myopia.
To correct myopia, we needed a diverging lens, as shown in FIGURE 35.10c, to slightly defocus the rays and move the image point back to the retina. To focus on a very distant object, the person needs a corrective lens that forms an upright, virtual image at her actual far point. That virtual image acts as an object for the eye itself and, when fully relaxed, the eye can focus these rays onto the retina.
EXAMPLE 35.4 Correcting hyperopia
Sanjay has hyperopia. The near point of his left eye is 150 cm. What prescription lens will restore normal vision?
MODEL Normal vision will allow Sanjay to focus on an object 25 cm away. In measuring distances, we’ll ignore the small space between the lens and his eye.
SOLVE Because Sanjay can see objects at 150 cm, using maximum accommodation, we want a lens that creates a virtual image at position (negative because it’s a virtual image) of an object held at . From the thin-lens equation,
is the lens power, and are diopters. Thus the prescription is for a lens with power .
REVIEW Hyperopia is always corrected with a converging lens.
EXAMPLE 35.5 Correcting myopia
Martina has myopia. The far point of her left eye is 200 cm. What prescription lens will restore normal vision?
MODEL Normal vision will allow Martina to focus on a very distant object. In measuring distances, we’ll ignore the small space between the lens and her eye.
SOLVE Because Martina can see objects at 200 cm with a fully relaxed eye, we want a lens that will create a virtual image at position (negative because it’s a virtual image) of a distant object at . From the thin-lens equation,
Thus the prescription is for a lens with power .
REVIEW Myopia is always corrected with a diverging lens.