26.10

The Human Eye

| Anatomy

Without doubt, the human eye is the most remarkable of all optical devices. Figure 26-34 shows some of its main anatomical features. The eyeball is approximately spherical with a diameter of about 25 mm. Light enters the eye through a transparent membrane (the cornea). This membrane covers a clear liquid region (the aqueous humor), behind which are a diaphragm (the iris), the lens, a region filled with a jelly-like substance (the vitreous humor), and, finally, the retina. The retina is the light-sensitive part of the eye, consisting of millions of structures called rods and cones. When stimulated by light, these structures send electrical impulses via the optic nerve to the brain, which interprets the image on the retina.

Figure 26-34 A cross-sectional view of the human eye.

The iris is the colored portion of the eye and controls the amount of light reaching the retina. The iris acts as a controller because it is a muscular diaphragm with a variable opening at its center, through which the light passes. The opening is called the pupil. The diameter of the pupil varies from about 2 to 7 mm, decreasing in bright light and increasing (dilating) in dim light.
Of prime importance to the operation of the eye is the fact that the lens is flexible, and its shape can be altered by the action of the ciliary muscle. The lens is connected to the ciliary muscle by the suspensory ligaments (see the drawing). We will see shortly how the shape-changing ability of the lens affects the focusing ability of the eye.

| Optics

Optically, the eye and the camera are similar; both have a lens system and a diaphragm with a variable opening or aperture at its center. Moreover, the retina of the eye and the film in the camera serve similar functions, for both record the image formed by the lens system. In the eye, the image formed on the retina is real, inverted, and smaller than the object, just as it is in a camera. Although the image on the retina is inverted, it is interpreted by the brain as being right-side up.

The physics of the human eye.

For clear vision, the eye must refract the incoming light rays, so as to form a sharp image on the retina. In reaching the retina, the light travels through five different media, each with a different index of refraction n: air (n = 1.00), the cornea (n = 1.38), the aqueous humor (n = 1.33), the lens (n = 1.40, on the average), and the vitreous humor (n = 1.34). Each time light passes from one medium into another, it is refracted at the boundary. The greatest amount of refraction, about 70% or so, occurs at the air/cornea boundary. According to Snell’s law, the large refraction at this interface occurs primarily because the refractive index of air (n = 1.00) is so different from that of the cornea (n = 1.38). The refraction at all the other boundaries is relatively small because the indices of refraction on either side of these boundaries are nearly equal. The lens itself contributes only about 20–25% of the total refraction, since the surrounding aqueous and vitreous humors have indices of refraction that are nearly the same as that of the lens.
Even though the lens contributes only a quarter of the total refraction or less, its function is an important one. The eye has a fixed image distance; that is, the distance between the lens and the retina is constant. Therefore, the only way that objects located at different distances can produce images on the retina is for the focal length of the lens to be adjustable. And it is the ciliary muscle that adjusts the focal length. When the eye looks at a very distant object, the ciliary muscle is not tensed. The lens has its least curvature and, consequently, its longest focal length. Under this condition the eye is said to be “fully relaxed,” and the rays form a sharp image on the retina, as in Figure 26-35a. When the object moves closer to the eye, the ciliary muscle tenses automatically, thereby increasing the curvature of the lens, shortening the focal length, and permitting a sharp image to form again on the retina (Figure 26-35b). When a sharp image of an object is formed on the retina, we say the eye is “focused” on the object. The process in which the lens changes its focal length to focus on objects at different distances is called accommodation.

Figure 26-35 (a) When fully relaxed, the lens of the eye has its longest focal length, and an image of a very distant object is formed on the retina. (b) When the ciliary muscle is tensed, the lens has a shorter focal length. Consequently, an image of a closer object is also formed on the retina.

When you hold a book too close, the print is blurred because the lens cannot adjust enough to bring the book into focus. The point nearest the eye at which an object can be placed and still produce a sharp image on the retina is called the near point of the eye. The ciliary muscle is fully tensed when an object is placed at the near point. For people in their early twenties with normal vision, the near point is located about 25 cm from the eye. It increases to about 50 cm at age 40 and to roughly 500 cm at age 60. Since most reading material is held at a distance of 25–45 cm from the eye, older adults typically need eyeglasses to overcome the loss of accommodation. The far point of the eye is the location of the farthest object on which the fully relaxed eye can focus. A person with normal eyesight can see objects very far away, such as the planets and stars, and thus has a far point located nearly at infinity.

| Nearsightedness

A person who is nearsighted (myopic) can focus on nearby objects but cannot clearly see objects far away. For such a person, the far point of the eye is not at infinity and may even be as close to the eye as three or four meters. When a nearsighted eye tries to focus on a distant object, the eye is fully relaxed, like a normal eye. However, the nearsighted eye has a focal length that is shorter than it should be, so rays from the distant object form a sharp image in front of the retina, as Figure 26-36a shows, and blurred vision results.

Figure 26-36 (a) When a nearsighted person views a distant object, the image is formed in front of the retina. The result is blurred vision. (b) With a diverging lens in front of the eye, the image is moved onto the retina and clear vision results. (c) The diverging lens is designed to form a virtual image at the far point of the nearsighted eye.

The physics of nearsightedness.

The nearsighted eye can be corrected with glasses or contacts that use diverging lenses, as Figure 26-36b suggests. The rays from the object diverge after leaving the eyeglass lens. Therefore, when they are subsequently refracted toward the principal axis by the eye, a sharp image is formed farther back and falls on the retina. Since the relaxed (but nearsighted) eye can focus on an object at the eye’s far point—but not on objects farther away—the diverging lens is designed to transform a very distant object into an image located at the far point. Part c of the drawing shows this transformation, and the next example illustrates how to determine the focal length of the diverging lens that accomplishes it.

| Example 12 | | | Eyeglasses for the Nearsighted Person

A nearsighted person has a far point located only 521 cm from the eye. Assuming that eye-glasses are to be worn 2 cm in front of the eye, find the focal length needed for the diverging lenses of the glasses so the person can see distant objects.
Reasoning In Figure 26-36c the far point is 521 cm away from the eye. Since the glasses are worn 2 cm from the eye, the far point is 519 cm to the left of the diverging lens. The image distance, then, is −519 cm, the negative sign indicating that the image is a virtual image formed to the left of the lens. The object is assumed to be infinitely far from the diverging lens. The thin-lens equation can be used to find the focal length of the eyeglasses. We expect the focal length to be negative, since the lens is a diverging lens.

Problem solving insight Eyeglasses are worn about 2 cm from the eyes. Be sure, if necessary, to take this 2 cm into account when determining the object and image distances (do and di) that are used in the thin-lens equation.

Solution With di = −519 cm and , the focal length can be found as follows:

| (26.6)

The value for f is negative, as expected for a diverging lens.

| Farsightedness

A farsighted (hyperopic) person can usually see distant objects clearly, but cannot focus on those nearby. Whereas the near point of a young and normal eye is located about 25 cm from the eye, the near point of a farsighted eye may be considerably farther away than that, perhaps as far as several hundred centimeters. When a farsighted eye tries to focus on a book held closer than the near point, it accommodates and shortens its focal length as much as it can. However, even at its shortest, the focal length is longer than it should be. Therefore, the light rays from the book would form a sharp image behind the retina if they could do so, as Figure 26-37a suggests. In reality, no light passes through the retina, but a blurred image does form on it.

Figure 26-37 (a) When a farsighted person views an object located inside the near point, a sharp image would be formed behind the retina if light could pass through it. Only a blurred image forms on the retina. (b) With a converging lens in front of the eye, the sharp image is moved onto the retina and clear vision results. (c) The converging lens is designed to form a virtual image at the near point of the farsighted eye.

The physics of farsightedness.

Figure 26-37b shows that farsightedness can be corrected by placing a converging lens in front of the eye. The lens refracts the light rays more toward the principal axis before they enter the eye. Consequently, when the rays are refracted even more by the eye, they converge to form an image on the retina. Part c of the figure illustrates what the eye sees when it looks through the converging lens. The lens is designed so that the eye perceives the light to be coming from a virtual image located at the near point. Example 13 shows how the focal length of the converging lens is determined to correct for farsightedness.

| Example 13 | | | Contact Lenses for the Farsighted Person

A farsighted person has a near point located 210 cm from the eyes. Obtain the focal length of the converging lenses in a pair of contacts that can be used to read a book held 25.0 cm from the eyes. Reasoning A contact lens is placed directly against the eye. Thus, the object distance, which is the distance from the book to the lens, is 25.0 cm. The lens forms an image of the book at the near point of the eye, so the image distance is −210 cm. The minus sign indicates that the image is a virtual image formed to the left of the lens, as in Figure 26-37c. The focal length can be obtained from the thin-lens equation.
Solution With do = 25.0 cm and di = −210 cm, the focal length can be determined from the thin-lens equation as follows:

| The Refractive Power of a Lens–The Diopter

The extent to which rays of light are refracted by a lens depends on its focal length. However, the optometrists who prescribe correctional lenses and the opticians who make lenses do not specify the focal length directly in prescriptions. Instead, they use the concept of refractive power to describe the extent to which a lens refracts light:

| (26.8)

The refractive power is measured in units of diopters. One diopter is 1 m−1.
Equation 26.8 shows that a converging lens has a refractive power of 1 diopter if it focuses parallel light rays to a focal point 1 m beyond the lens. If a lens refracts parallel rays even more and converges them to a focal point only 0.25 m beyond the lens, the lens has four times more refractive power, or 4 diopters. Since a converging lens has a positive focal length and a diverging lens has a negative focal length, the refractive power of a converging lens is positive while that of a diverging lens is negative. For instance, the eyeglasses in Example 12 would be described in a prescription from an optometrist in the following way: . The contact lenses in Example 13 would be described in a similar fashion: .

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.