I. Optics of Vision
Physical Principles of Optics
Before it is possible to understand the optical system of the eye, the student must first be thoroughly familiar with the basic principles of optics, including the physics of light refraction, focusing, depth of focus, and so forth. A brief review of these physical principles is presented; then the optics of the eye is discussed.
Refraction of Light
Refractive Index of a Transparent Substance
Light rays travel through air at a velocity of about 300,000 km/sec, but they travel much slower through transparent solids and liquids. The refractive index of a transparent substance is the ratio of the velocity of light in air to the velocity in the substance. The refractive index of air itself is 1.00. Thus, if light travels through a particular type of glass at a velocity of 200,000 km/sec, the refractive index of this glass is 300,000 divided by 200,000, or 1.50.
Refraction of Light Rays at an Interface Between Two Media with Different Refractive Indices
When light rays traveling forward in a beam (as shown in Figure 49-1A) strike an interface that is perpendicular to the beam, the rays enter the second medium without deviating from their course. The only effect that occurs is decreased velocity of transmission and shorter wavelength, as shown in the figure by the shorter distances between wave fronts.
Figure 49-1 Light rays entering a glass surface perpendicular to the light rays (A) and a glass surface angulated to the light rays (B). This figure demonstrates that the distance between waves after they enter the glass is shortened to about two-thirds that in air. It also shows that light rays striking an angulated glass surface are bent.
If the light rays pass through an angulated interface as shown in Figure 49-1B, the rays bend if the refractive indices of the two media are different from each other. In this particular figure, the light rays are leaving air, which has a refractive index of 1.00, and are entering a block of glass having a refractive index of 1.50. When the beam first strikes the angulated interface, the lower edge of the beam enters the glass ahead of the upper edge. The wave front in the upper portion of the beam continues to travel at a velocity of 300,000 km/sec, while that which entered the glass travels at a velocity of 200,000 km/sec. This causes the upper portion of the wave front to move ahead of the lower portion so that the wave front is no longer vertical but angulated to the right. Because the direction in which light travels is always perpendicular to the plane of the wave front, the direction of travel of the light beam bends downward.
This bending of light rays at an angulated interface is known as refraction. Note particularly that the degree of refraction increases as a function of (1) the ratio of the two refractive indices of the two transparent media and (2) the degree of angulation between the interface and the entering wave front.
Application of Refractive Principles to Lenses
Convex Lens Focuses Light Rays
Figure 49-2 shows parallel light rays entering a convex lens. The light rays passing through the center of the lens strike the lens exactly perpendicular to the lens surface and, therefore, pass through the lens without being refracted. Toward either edge of the lens, however, the light rays strike a progressively more angulated interface. The outer rays bend more and more toward the center, which is called convergence of the rays. Half the bending occurs when the rays enter the lens, and half as they exit from the opposite side. If the lens has exactly the proper curvature, parallel light rays passing through each part of the lens will be bent exactly enough so that all the rays will pass through a single point, which is called the focal point.
Figure 49-2 Bending of light rays at each surface of a convex spherical lens, showing that parallel light rays are focused to a focal point.
Concave Lens Diverges Light Rays
Figure 49-3 shows the effect of a concave lens on parallel light rays. The rays that enter the center of the lens strike an interface that is perpendicular to the beam and, therefore, do not refract. The rays at the edge of the lens enter the lens ahead of the rays in the center. This is opposite to the effect in the convex lens, and it causes the peripheral light rays to diverge from the light rays that pass through the center of the lens. Thus, the concave lens diverges light rays, but the convex lens converges light rays.
Figure 49-3 Bending of light rays at each surface of a concave spherical lens, showing that parallel light rays are diverged.
Cylindrical Lens Bends Light Rays in Only One Plane—Comparison with Spherical Lenses
Figure 49-4 shows both a convex spherical lens and a convex cylindrical lens. Note that the cylindrical lens bends light rays from the two sides of the lens but not from the top or the bottom. That is, bending occurs in one plane but not the other. Thus, parallel light rays are bent to a focal line. Conversely, light rays that pass through the spherical lens are refracted at all edges of the lens (in both planes) toward the central ray, and all the rays come to a focal point.
Figure 49-4 A, Point focus of parallel light rays by a spherical convex lens. B, Line focus of parallel light rays by a cylindrical convex lens.
The cylindrical lens is well demonstrated by a test tube full of water. If the test tube is placed in a beam of sunlight and a piece of paper is brought progressively closer to the opposite side of the tube, a certain distance will be found at which the light rays come to a focal line. The spherical lens is demonstrated by an ordinary magnifying glass. If such a lens is placed in a beam of sunlight and a piece of paper is brought progressively closer to the lens, the light rays will impinge on a common focal point at an appropriate distance.
Concave cylindrical lenses diverge light rays in only one plane in the same manner that convex cylindrical lenses converge light rays in one plane.
Combination of Two Cylindrical Lenses at Right Angles Equals a Spherical Lens
Figure 49-5B shows two convex cylindrical lenses at right angles to each other. The vertical cylindrical lens converges the light rays that pass through the two sides of the lens, and the horizontal lens converges the top and bottom rays. Thus, all the light rays come to a single-point focus. In other words, two cylindrical lenses crossed at right angles to each other perform the same function as one spherical lens of the same refractive power.
Figure 49-5 A, Focusing of light from a point source to a line focus by a cylindrical lens. B, Two cylindrical convex lenses at right angles to each other, demonstrating that one lens converges light rays in one plane and the other lens converges light rays in the plane at a right angle. The two lenses combined give the same point focus as that obtained with a single spherical convex lens.
Focal Length of a Lens
The distance beyond a convex lens at which parallel rays converge to a common focal point is called the focal length of the lens. The diagram at the top of Figure 49-6 demonstrates this focusing of parallel light rays.
Figure 49-6 The two upper lenses of this figure have the same focal length, but the light rays entering the top lens are parallel, whereas those entering the middle lens are diverging; the effect of parallel versus diverging rays on the focal distance is shown. The bottom lens has far more refractive power than either of the other two lenses (i.e., has a much shorter focal length), demonstrating that the stronger the lens is, the nearer to the lens the point focus is.
In the middle diagram, the light rays that enter the convex lens are not parallel but are diverging because the origin of the light is a point source not far away from the lens itself. Because these rays are diverging outward from the point source, it can be seen from the diagram that they do not focus at the same distance away from the lens as do parallel rays. In other words, when rays of light that are already diverging enter a convex lens, the distance of focus on the other side of the lens is farther from the lens than is the focal length of the lens for parallel rays.
The bottom diagram of Figure 49-6 shows light rays that are diverging toward a convex lens that has far greater curvature than that of the other two lenses in the figure. In this diagram, the distance from the lens at which the light rays come to focus is exactly the same as that from the lens in the first diagram, in which the lens is less convex but the rays entering it are parallel. This demonstrates that both parallel rays and diverging rays can be focused at the same distance beyond a lens, provided the lens changes its convexity.
The relation of focal length of the lens, distance of the point source of light, and distance of focus is expressed by the following formula:
in which f is the focal length of the lens for parallel rays, a is the distance of the point source of light from the lens, and b is the distance of focus on the other side of the lens.
Formation of an Image by a Convex Lens
Figure 49-7A shows a convex lens with two point sources of light to the left. Because light rays pass through the center of a convex lens without being refracted in either direction, the light rays from each point source of light are shown to come to a point focus on the opposite side of the lens directly in line with the point source and the center of the lens.
Figure 49-7 A, Two point sources of light focused at two separate points on opposite sides of the lens. B, Formation of an image by a convex spherical lens.
Any object in front of the lens is, in reality, a mosaic of point sources of light. Some of these points are very bright, some are very weak, and they vary in color. Each point source of light on the object comes to a separate point focus on the opposite side of the lens in line with the lens center. If a white sheet of paper is placed at the focus distance from the lens, one can see an image of the object, as demonstrated in Figure 49-7B. However, this image is upside down with respect to the original object, and the two lateral sides of the image are reversed. This is the method by which the lens of a camera focuses images on film.
Measurement of the Refractive Power of a Lens—“Diopter”
The more a lens bends light rays, the greater is its “refractive power.” This refractive power is measured in terms of diopters. The refractive power in diopters of a convex lens is equal to 1 meter divided by its focal length. Thus, a spherical lens that converges parallel light rays to a focal point 1 meter beyond the lens has a refractive power of +1 diopter, as shown in Figure 49-8. If the lens is capable of bending parallel light rays twice as much as a lens with a power of +1 diopter, it is said to have a strength of +2 diopters, and the light rays come to a focal point 0.5 meter beyond the lens. A lens capable of converging parallel light rays to a focal point only 10 centimeters (0.10 meter) beyond the lens has a refractive power of +10 diopters.
Figure 49-8 Effect of lens strength on the focal distance.
The refractive power of concave lenses cannot be stated in terms of the focal distance beyond the lens because the light rays diverge, rather than focus to a point. However, if a concave lens diverges light rays at the same rate that a 1-diopter convex lens converges them, the concave lens is said to have a dioptric strength of −1. Likewise, if the concave lens diverges light rays as much as a +10-diopter lens converges them, this lens is said to have a strength of −10 diopters.
Concave lenses “neutralize” the refractive power of convex lenses. Thus, placing a 1-diopter concave lens immediately in front of a 1-diopter convex lens results in a lens system with zero refractive power.
The strengths of cylindrical lenses are computed in the same manner as the strengths of spherical lenses, except that the axis of the cylindrical lens must be stated in addition to its strength. If a cylindrical lens focuses parallel light rays to a line focus 1 meter beyond the lens, it has a strength of +1 diopter. Conversely, if a cylindrical lens of a concave type diverges light rays as much as a +1-diopter cylindrical lens converges them, it has a strength of −1 diopter. If the focused line is horizontal, its axis is said to be 0 degrees. If it is vertical, its axis is 90 degrees.
Optics of the Eye
The Eye as a Camera
The eye, shown in Figure 49-9, is optically equivalent to the usual photographic camera. It has a lens system, a variable aperture system (the pupil), and a retina that corresponds to the film. The lens system of the eye is composed of four refractive interfaces: (1) the interface between air and the anterior surface of the cornea, (2) the interface between the posterior surface of the cornea and the aqueous humor, (3) the interface between the aqueous humor and the anterior surface of the lens of the eye, and (4) the interface between the posterior surface of the lens and the vitreous humor. The internal index of air is 1; the cornea, 1.38; the aqueous humor, 1.33; the crystalline lens (on average), 1.40; and the vitreous humor, 1.34.
Figure 49-9 The eye as a camera. The numbers are the refractive indices.
Consideration of All Refractive Surfaces of the Eye as a Single Lens—The “Reduced” Eye
If all the refractive surfaces of the eye are algebraically added together and then considered to be one single lens, the optics of the normal eye may be simplified and represented schematically as a “reduced eye.” This is useful in simple calculations. In the reduced eye, a single refractive surface is considered to exist, with its central point 17 millimeters in front of the retina and a total refractive power of 59 diopters when the lens is accommodated for distant vision.
About two thirds of the 59 diopters of refractive power of the eye is provided by the anterior surface of the cornea (not by the eye lens). The principal reason for this is that the refractive index of the cornea is markedly different from that of air, whereas the refractive index of the eye lens is not greatly different from the indices of the aqueous humor and vitreous humor.
The total refractive power of the internal lens of the eye, as it normally lies in the eye surrounded by fluid on each side, is only 20 diopters, about one-third the total refractive power of the eye. But the importance of the internal lens is that, in response to nervous signals from the brain, its curvature can be increased markedly to provide “accommodation,” which is discussed later in the chapter.
Formation of an Image on the Retina
In the same manner that a glass lens can focus an image on a sheet of paper, the lens system of the eye can focus an image on the retina. The image is inverted and reversed with respect to the object. However, the mind perceives objects in the upright position despite the upside-down orientation on the retina because the brain is trained to consider an inverted image as normal.
Mechanism of “Accommodation”
In children, the refractive power of the lens of the eye can be increased voluntarily from 20 diopters to about 34 diopters; this in an “accommodation” of 14 diopters. To do this, the shape of the lens is changed from that of a moderately convex lens to that of a very convex lens. The mechanism is as follows.
In a young person, the lens is composed of a strong elastic capsule filled with viscous, proteinaceous, but transparent fluid. When the lens is in a relaxed state with no tension on its capsule, it assumes an almost spherical shape, owing mainly to the elastic retraction of the lens capsule. However, as shown in Figure 49-10, about 70 suspensory ligaments attach radially around the lens, pulling the lens edges toward the outer circle of the eyeball. These ligaments are constantly tensed by their attachments at the anterior border of the choroid and retina. The tension on the ligaments causes the lens to remain relatively flat under normal conditions of the eye.
Figure 49-10 Mechanism of accommodation (focusing).
However, also located at the lateral attachments of the lens ligaments to the eyeball is the ciliary muscle, which itself has two separate sets of smooth muscle fibers—meridional fibers and circular fibers. The meridional fibers extend from the peripheral ends of the suspensory ligaments to the corneoscleral junction. When these muscle fibers contract, the peripheral insertions of the lens ligaments are pulled medially toward the edges of the cornea, thereby releasing the ligaments’ tension on the lens. The circular fibers are arranged circularly all the way around the ligament attachments so that when they contract, a sphincter-like action occurs, decreasing the diameter of the circle of ligament attachments; this also allows the ligaments to pull less on the lens capsule.
Thus, contraction of either set of smooth muscle fibers in the ciliary muscle relaxes the ligaments to the lens capsule, and the lens assumes a more spherical shape, like that of a balloon, because of the natural elasticity of the lens capsule.
Accommodation Is Controlled by Parasympathetic Nerves
The ciliary muscle is controlled almost entirely by parasympathetic nerve signals transmitted to the eye through the third cranial nerve from the third nerve nucleus in the brain stem, as explained in Chapter 51. Stimulation of the parasympathetic nerves contracts both sets of ciliary muscle fibers, which relaxes the lens ligaments, thus allowing the lens to become thicker and increase its refractive power. With this increased refractive power, the eye focuses on objects nearer than when the eye has less refractive power. Consequently, as a distant object moves toward the eye, the number of parasympathetic impulses impinging on the ciliary muscle must be progressively increased for the eye to keep the object constantly in focus. (Sympathetic stimulation has an additional effect in relaxing the ciliary muscle, but this effect is so weak that it plays almost no role in the normal accommodation mechanism; the neurology of this is discussed in Chapter 51.)
Presbyopia—Loss of Accommodation by the Lens
As a person grows older, the lens grows larger and thicker and becomes far less elastic, partly because of progressive denaturation of the lens proteins. The ability of the lens to change shape decreases with age. The power of accommodation decreases from about 14 diopters in a child to less than 2 diopters by the time a person reaches 45 to 50 years; it then decreases to essentially 0 diopters at age 70 years. Thereafter, the lens remains almost totally nonaccommodating, a condition known as “presbyopia.”
Once a person has reached the state of presbyopia, each eye remains focused permanently at an almost constant distance; this distance depends on the physical characteristics of each person’s eyes. The eyes can no longer accommodate for both near and far vision. To see clearly both in the distance and nearby, an older person must wear bifocal glasses with the upper segment focused for far-seeing and the lower segment focused for near-seeing (e.g., for reading).
The major function of the iris is to increase the amount of light that enters the eye during darkness and to decrease the amount of light that enters the eye in daylight. The reflexes for controlling this mechanism are considered in the discussion of the neurology of the eye in Chapter 51.
The amount of light that enters the eye through the pupil is proportional to the area of the pupil or to the square of the diameter of the pupil. The pupil of the human eye can become as small as about 1.5 millimeters and as large as 8 millimeters in diameter. The quantity of light entering the eye can change about 30-fold as a result of changes in pupillary aperture.
“Depth of Focus” of the Lens System Increases with Decreasing Pupillary Diameter
Figure 49-11 shows two eyes that are exactly alike except for the diameters of the pupillary apertures. In the upper eye, the pupillary aperture is small, and in the lower eye, the aperture is large. In front of each of these two eyes are two small point sources of light; light from each passes through the pupillary aperture and focuses on the retina. Consequently, in both eyes, the retina sees two spots of light in perfect focus. It is evident from the diagrams, however, that if the retina is moved forward or backward to an out-of-focus position, the size of each spot will not change much in the upper eye, but in the lower eye the size of each spot will increase greatly, becoming a “blur circle.” In other words, the upper lens system has far greater depth of focus than the bottom lens system. When a lens system has great depth of focus, the retina can be displaced considerably from the focal plane or the lens strength can change considerably from normal and the image will still remain nearly in sharp focus, whereas when a lens system has a “shallow” depth of focus, moving the retina only slightly away from the focal plane causes extreme blurring.
Figure 49-11 Effect of small (top) and large (bottom) pupillary apertures on “depth of focus.”
The greatest possible depth of focus occurs when the pupil is extremely small. The reason for this is that, with a very small aperture, almost all the rays pass through the center of the lens, and the central-most rays are always in focus, as explained earlier.
Errors of Refraction
Emmetropia (Normal Vision)
As shown in Figure 49-12, the eye is considered to be normal, or “emmetropic,” if parallel light rays from distant objects are in sharp focus on the retina when the ciliary muscle is completely relaxed. This means that the emmetropic eye can see all distant objects clearly with its ciliary muscle relaxed. However, to focus objects at close range, the eye must contract its ciliary muscle and thereby provide appropriate degrees of accommodation.
Figure 49-12 Parallel light rays focus on the retina in emmetropia, behind the retina in hyperopia, and in front of the retina in myopia.
Hyperopia, which is also known as “farsightedness,” is usually due to either an eyeball that is too short or, occasionally, a lens system that is too weak. In this condition, as seen in the middle panel of Figure 49-12, parallel light rays are not bent sufficiently by the relaxed lens system to come to focus by the time they reach the retina. To overcome this abnormality, the ciliary muscle must contract to increase the strength of the lens. By using the mechanism of accommodation, a farsighted person is capable of focusing distant objects on the retina. If the person has used only a small amount of strength in the ciliary muscle to accommodate for the distant objects, he or she still has much accommodative power left, and objects closer and closer to the eye can also be focused sharply until the ciliary muscle has contracted to its limit. In old age, when the lens becomes “presbyopic,” a farsighted person is often unable to accommodate the lens sufficiently to focus even distant objects, much less near objects.
In myopia, or “nearsightedness,” when the ciliary muscle is completely relaxed, the light rays coming from distant objects are focused in front of the retina, as shown in the bottom panel of Figure 49-12. This is usually due to too long an eyeball, but it can result from too much refractive power in the lens system of the eye.
No mechanism exists by which the eye can decrease the strength of its lens to less than that which exists when the ciliary muscle is completely relaxed. A myopic person has no mechanism by which to focus distant objects sharply on the retina. However, as an object moves nearer to the person’s eye, it finally gets close enough that its image can be focused. Then, when the object comes still closer to the eye, the person can use the mechanism of accommodation to keep the image focused clearly. A myopic person has a definite limiting “far point” for clear vision.
Correction of Myopia and Hyperopia by Use of Lenses
It will be recalled that light rays passing through a concave lens diverge. If the refractive surfaces of the eye have too much refractive power, as in myopia, this excessive refractive power can be neutralized by placing in front of the eye a concave spherical lens, which will diverge rays. Such correction is demonstrated in the upper diagram of Figure 49-13.
Figure 49-13 Correction of myopia with a concave lens, and correction of hyperopia with a convex lens.
Conversely, in a person who has hyperopia—that is, someone who has too weak a lens system—the abnormal vision can be corrected by adding refractive power using a convex lens in front of the eye. This correction is demonstrated in the lower diagram of Figure 49-13.
One usually determines the strength of the concave or convex lens needed for clear vision by “trial and error”—that is, by trying first a strong lens and then a stronger or weaker lens until the one that gives the best visual acuity is found.
Astigmatism is a refractive error of the eye that causes the visual image in one plane to focus at a different distance from that of the plane at right angles. This most often results from too great a curvature of the cornea in one plane of the eye. An example of an astigmatic lens would be a lens surface like that of an egg lying sidewise to the incoming light. The degree of curvature in the plane through the long axis of the egg is not nearly as great as the degree of curvature in the plane through the short axis.
Because the curvature of the astigmatic lens along one plane is less than the curvature along the other plane, light rays striking the peripheral portions of the lens in one plane are not bent nearly as much as the rays striking the peripheral portions of the other plane. This is demonstrated in Figure 49-14, which shows rays of light originating from a point source and passing through an oblong, astigmatic lens. The light rays in the vertical plane, indicated by plane BD, are refracted greatly by the astigmatic lens because of the greater curvature in the vertical direction than in the horizontal direction. By contrast, the light rays in the horizontal plane, indicated by plane AC, are not bent nearly as much as the light rays in vertical plane BD. It is obvious that light rays passing through an astigmatic lens do not all come to a common focal point because the light rays passing through one plane focus far in front of those passing through the other plane.
Figure 49-14 Astigmatism, demonstrating that light rays focus at one focal distance in one focal plane (plane AC) and at another focal distance in the plane at a right angle (plane BD).
The accommodative power of the eye can never compensate for astigmatism because, during accommodation, the curvature of the eye lens changes approximately equally in both planes; therefore, in astigmatism, each of the two planes requires a different degree of accommodation. Thus, without the aid of glasses, a person with astigmatism never sees in sharp focus.
Correction of Astigmatism with a Cylindrical Lens
One may consider an astigmatic eye as having a lens system made up of two cylindrical lenses of different strengths and placed at right angles to each other. To correct for astigmatism, the usual procedure is to find a spherical lens by trial and error that corrects the focus in one of the two planes of the astigmatic lens. Then an additional cylindrical lens is used to correct the remaining error in the remaining plane. To do this, both the axis and the strength of the required cylindrical lens must be determined.
Several methods exist for determining the axis of the abnormal cylindrical component of the lens system of an eye. One of these methods is based on the use of parallel black bars of the type shown in Figure 49-15. Some of these parallel bars are vertical, some horizontal, and some at various angles to the vertical and horizontal axes. After placing various spherical lenses in front of the astigmatic eye, a strength of lens that causes sharp focus of one set of parallel bars but does not correct the fuzziness of the set of bars at right angles to the sharp bars is usually found. It can be shown from the physical principles of optics discussed earlier in this chapter that the axis of the out-of-focuscylindrical component of the optical system is parallel to the bars that are fuzzy. Once this axis is found, the examiner tries progressively stronger and weaker positive or negative cylindrical lenses, the axes of which are placed in line with the out-of-focus bars, until the patient sees all the crossed bars with equal clarity. When this has been accomplished, the examiner directs the optician to grind a special lens combining both the spherical correction and the cylindrical correction at the appropriate axis.
Figure 49-15 Chart composed of parallel black bars at different angular orientations for determining the axis of astigmatism.
Correction of Optical Abnormalities by Use of Contact Lenses
Glass or plastic contact lenses that fit snugly against the anterior surface of the cornea can be inserted. These lenses are held in place by a thin layer of tear fluid that fills the space between the contact lens and the anterior eye surface.
A special feature of the contact lens is that it nullifies almost entirely the refraction that normally occurs at the anterior surface of the cornea. The reason for this is that the tears between the contact lens and the cornea have a refractive index almost equal to that of the cornea, so the anterior surface of the cornea no longer plays a significant role in the eye’s optical system. Instead, the outer surface of the contact lens plays the major role. Thus, the refraction of this surface of the contact lens substitutes for the cornea’s usual refraction. This is especially important in people whose eye refractive errors are caused by an abnormally shaped cornea, such as those who have an odd-shaped, bulging cornea—a condition called keratoconus. Without the contact lens, the bulging cornea causes such severe abnormality of vision that almost no glasses can correct the vision satisfactorily; when a contact lens is used, however, the corneal refraction is neutralized and normal refraction by the outer surface of the contact lens is substituted.
The contact lens has several other advantages as well, including (1) the lens turns with the eye and gives a broader field of clear vision than glasses do, and (2) the contact lens has little effect on the size of the object the person sees through the lens, whereas lenses placed 1 centimeter or so in front of the eye do affect the size of the image, in addition to correcting the focus.
Cataracts—Opaque Areas in the Lens
“Cataracts” are an especially common eye abnormality that occurs mainly in older people. A cataract is a cloudy or opaque area or areas in the lens. In the early stage of cataract formation, the proteins in some of the lens fibers become denatured. Later, these same proteins coagulate to form opaque areas in place of the normal transparent protein fibers.
When a cataract has obscured light transmission so greatly that it seriously impairs vision, the condition can be corrected by surgical removal of the lens. When this is done, the eye loses a large portion of its refractive power, which must be replaced by a powerful convex lens in front of the eye; usually, however, an artificial plastic lens is implanted in the eye in place of the removed lens.
Theoretically, light from a distant point source, when focused on the retina, should be infinitely small. However, because the lens system of the eye is never perfect, such a retinal spot ordinarily has a total diameter of about 11 micrometers, even with maximal resolution of the normal eye optical system. The spot is brightest in its center and shades off gradually toward the edges, as shown by the two-point images in Figure 49-16.
Figure 49-16 Maximum visual acuity for two-point sources of light.
The average diameter of the cones in the fovea of the retina—the central part of the retina, where vision is most highly developed—is about 1.5 micrometers, which is one-seventh the diameter of the spot of light. Nevertheless, because the spot of light has a bright center point and shaded edges, a person can normally distinguish two separate points if their centers lie up to 2 micrometers apart on the retina, which is slightly greater than the width of a foveal cone. This discrimination between points is also shown in Figure 49-16.
The normal visual acuity of the human eye for discriminating between point sources of light is about 25 seconds of arc. That is, when light rays from two separate points strike the eye with an angle of at least 25 seconds between them, they can usually be recognized as two points instead of one. This means that a person with normal visual acuity looking at two bright pinpoint spots of light 10 meters away can barely distinguish the spots as separate entities when they are 1.5 to 2 millimeters apart.
The fovea is less than 0.5 millimeter (<500 micrometers) in diameter, which means that maximum visual acuity occurs in less than 2 degrees of the visual field. Outside this foveal area, the visual acuity becomes progressively poorer, decreasing more than 10-fold as the periphery is approached. This is caused by the connection of more and more rods and cones to each optic nerve fiber in the nonfoveal, more peripheral parts of the retina, as discussed in Chapter 51.
Clinical Method for Stating Visual Acuity
The chart for testing eyes usually consists of letters of different sizes placed 20 feet away from the person being tested. If the person can see well the letters of a size that he or she should be able to see at 20 feet, the person is said to have 20/20 vision—that is, normal vision. If the person can see only letters that he or she should be able to see at 200 feet, the person is said to have 20/200 vision. In other words, the clinical method for expressing visual acuity is to use a mathematical fraction that expresses the ratio of two distances, which is also the ratio of one’s visual acuity to that of a person with normal visual acuity.
Determination of Distance of an Object from the Eye—“Depth Perception”
A person normally perceives distance by three major means: (1) the sizes of the images of known objects on the retina, (2) the phenomenon of moving parallax, and (3) the phenomenon of stereopsis. This ability to determine distance is called depth perception.
Determination of Distance by Sizes of Retinal Images of Known Objects
If one knows that a person being viewed is 6 feet tall, one can determine how far away the person is simply by the size of the person’s image on the retina. One does not consciously think about the size, but the brain has learned to calculate automatically from image sizes the distances of objects when the dimensions are known.
Determination of Distance by Moving Parallax
Another important means by which the eyes determine distance is that of moving parallax. If an individual looks off into the distance with the eyes completely still, he or she perceives no moving parallax, but when the person moves his or her head to one side or the other, the images of close-by objects move rapidly across the retinas, while the images of distant objects remain almost completely stationary. For instance, by moving the head 1 inch to the side when the object is only 1 inch in front of the eye, the image moves almost all the way across the retinas, whereas the image of an object 200 feet away from the eyes does not move perceptibly. Thus, by using this mechanism of moving parallax, one can tell the relative distances of different objects even though only one eye is used.
Determination of Distance by Stereopsis—Binocular Vision
Another method by which one perceives parallax is that of “binocular vision.” Because one eye is a little more than 2 inches to one side of the other eye, the images on the two retinas are different from each other. For instance, an object 1 inch in front of the nose forms an image on the left side of the retina of the left eye but on the right side of the retina of the right eye, whereas a small object 20 feet in front of the nose has its image at closely corresponding points in the centers of the two retinas. This type of parallax is demonstrated in Figure 49-17, which shows the images of a red spot and a yellow square actually reversed on the two retinas because they are at different distances in front of the eyes. This gives a type of parallax that is present all the time when both eyes are being used. It is almost entirely this binocular parallax (or stereopsis) that gives a person with two eyes far greater ability to judge relative distances when objects are nearby than a person who has only one eye. However, stereopsis is virtually useless for depth perception at distances beyond 50 to 200 feet.
Figure 49-17 Perception of distance (1) by the size of the image on the retina and (2) as a result of stereopsis.
The ophthalmoscope is an instrument through which an observer can look into another person’s eye and see the retina with clarity. Although the ophthalmoscope appears to be a relatively complicated instrument, its principles are simple. The basic components are shown in Figure 49-18 and can be explained as follows.
Figure 49-18 Optical system of the ophthalmoscope.
If a bright spot of light is on the retina of an emmetropic eye, light rays from this spot diverge toward the lens system of the eye. After passing through the lens system, they are parallel with one another because the retina is located one focal length distance behind the lens system. Then, when these parallel rays pass into an emmetropic eye of another person, they focus again to a point focus on the retina of the second person, because his or her retina is also one focal length distance behind the lens. Any spot of light on the retina of the observed eye projects to a focal spot on the retina of the observing eye. Thus, if the retina of one person is made to emit light, the image of his or her retina will be focused on the retina of the observer, provided the two eyes are emmetropic and are simply looking into each other.
To make an ophthalmoscope, one need only devise a means for illuminating the retina to be examined. Then, the reflected light from that retina can be seen by the observer simply by putting the two eyes close to each other. To illuminate the retina of the observed eye, an angulated mirror or a segment of a prism is placed in front of the observed eye in such a manner, as shown in Figure 49-18, that light from a bulb is reflected into the observed eye. Thus, the retina is illuminated through the pupil, and the observer sees into the subject’s pupil by looking over the edge of the mirror or prism or through an appropriately designed prism.
It is clear that these principles apply only to people with completely emmetropic eyes. If the refractive power of either the observed eye or the observer’s eye is abnormal, it is necessary to correct the refractive power for the observer to see a sharp image of the observed retina. The usual ophthalmoscope has a series of very small lenses mounted on a turret so that the turret can be rotated from one lens to another until the correction for abnormal refraction is made by selecting a lens of appropriate strength. In normal young adults, natural accommodative reflexes occur, causing an approximate +2-diopter increase in strength of the lens of each eye. To correct for this, it is necessary that the lens turret be rotated to approximately −4-diopter correction.
Fluid System of the Eye—Intraocular Fluid
The eye is filled with intraocular fluid, which maintains sufficient pressure in the eyeball to keep it distended. Figure 49-19 demonstrates that this fluid can be divided into two portions—aqueous humor,which lies in front of the lens, and vitreous humor, which is between the posterior surface of the lens and the retina. The aqueous humor is a freely flowing fluid, whereas the vitreous humor, sometimes called the vitreous body, is a gelatinous mass held together by a fine fibrillar network composed primarily of greatly elongated proteoglycan molecules. Both water and dissolved substances can diffuse slowly in the vitreous humor, but there is little flow of fluid.
Figure 49-19 Formation and flow of fluid in the eye.
Aqueous humor is continually being formed and reabsorbed. The balance between formation and reabsorption of aqueous humor regulates the total volume and pressure of the intraocular fluid.
Formation of Aqueous Humor by the Ciliary Body
Aqueous humor is formed in the eye at an average rate of 2 to 3 microliters each minute. Essentially all of it is secreted by the ciliary processes, which are linear folds projecting from the ciliary body into the space behind the iris where the lens ligaments and ciliary muscle attach to the eyeball. A cross section of these ciliary processes is shown in Figure 49-20, and their relation to the fluid chambers of the eye can be seen in Figure 49-19. Because of their folded architecture, the total surface area of the ciliary processes is about 6 square centimeters in each eye—a large area, considering the small size of the ciliary body. The surfaces of these processes are covered by highly secretory epithelial cells, and immediately beneath them is a highly vascular area.
Figure 49-20 Anatomy of the ciliary processes. Aqueous humor is formed on surfaces.
Aqueous humor is formed almost entirely as an active secretion by the epithelium of the ciliary processes. Secretion begins with active transport of sodium ions into the spaces between the epithelial cells. The sodium ions pull chloride and bicarbonate ions along with them to maintain electrical neutrality. Then all these ions together cause osmosis of water from the blood capillaries lying below into the same epithelial intercellular spaces, and the resulting solution washes from the spaces of the ciliary processes into the anterior chamber of the eye. In addition, several nutrients are transported across the epithelium by active transport or facilitated diffusion; they include amino acids, ascorbic acid, and glucose.
Outflow of Aqueous Humor from the Eye
After aqueous humor is formed by the ciliary processes, it first flows, as shown in Figure 49-19, through the pupil into the anterior chamber of the eye. From here, the fluid flows anterior to the lens and into the angle between the cornea and the iris, then through a meshwork of trabeculae, finally entering the canal of Schlemm, which empties into extraocular veins. Figure 49-21 demonstrates the anatomical structures at this iridocorneal angle, showing that the spaces between the trabeculae extend all the way from the anterior chamber to the canal of Schlemm. The canal of Schlemm is a thin-walled vein that extends circumferentially all the way around the eye. Its endothelial membrane is so porous that even large protein molecules, as well as small particulate matter up to the size of red blood cells, can pass from the anterior chamber into the canal of Schlemm. Even though the canal of Schlemm is actually a venous blood vessel, so much aqueous humor normally flows into it that it is filled only with aqueous humor rather than with blood. The small veins that lead from the canal of Schlemm to the larger veins of the eye usually contain only aqueous humor, and they are called aqueous veins.
Figure 49-21 Anatomy of the iridocorneal angle, showing the system for outflow of aqueous humor from the eyeball into the conjunctival veins.
The average normal intraocular pressure is about 15 mm Hg, with a range from 12 to 20 mm Hg.
Because it is impractical to pass a needle into a patient’s eye to measure intraocular pressure, this pressure is measured clinically by using a “tonometer,” the principle of which is shown in Figure 49-22. The cornea of the eye is anesthetized with a local anesthetic, and the footplate of the tonometer is placed on the cornea. A small force is then applied to a central plunger, causing the part of the cornea beneath the plunger to be displaced inward. The amount of displacement is recorded on the scale of the tonometer, and this is calibrated in terms of intraocular pressure.
Figure 49-22 Principles of the tonometer.
Regulation of Intraocular Pressure
Intraocular pressure remains constant in the normal eye, usually within ±2 mm Hg of its normal level, which averages about 15 mm Hg. The level of this pressure is determined mainly by the resistance to outflow of aqueous humor from the anterior chamber into the canal of Schlemm. This outflow resistance results from the meshwork of trabeculae through which the fluid must percolate on its way from the lateral angles of the anterior chamber to the wall of the canal of Schlemm. These trabeculae have minute openings of only 2 to 3 micrometers. The rate of fluid flow into the canal increases markedly as the pressure rises. At about 15 mm Hg in the normal eye, the amount of fluid leaving the eye by way of the canal of Schlemm usually averages 2.5 μl/min and equals the inflow of fluid from the ciliary body. The pressure normally remains at about this level of 15 mm Hg.
Mechanism for Cleansing the Trabecular Spaces and Intraocular Fluid
When large amounts of debris are present in the aqueous humor, as occurs after hemorrhage into the eye or during intraocular infection, the debris is likely to accumulate in the trabecular spaces leading from the anterior chamber to the canal of Schlemm; this debris can prevent adequate reabsorption of fluid from the anterior chamber, sometimes causing “glaucoma,” as explained subsequently. However, on the surfaces of the trabecular plates are large numbers of phagocytic cells. Immediately outside the canal of Schlemm is a layer of interstitial gel that contains large numbers of reticuloendothelial cells that have an extremely high capacity for engulfing debris and digesting it into small molecular substances that can then be absorbed. Thus, this phagocytic system keeps the trabecular spaces cleaned. The surface of the iris and other surfaces of the eye behind the iris are covered with an epithelium that is capable of phagocytizing proteins and small particles from the aqueous humor, thereby helping to maintain a clear fluid.
“Glaucoma”—a Principal Cause of Blindness
Glaucoma is one of the most common causes of blindness. It is a disease of the eye in which the intraocular pressure becomes pathologically high, sometimes rising acutely to 60 to 70 mm Hg. Pressures above 25 to 30 mm Hg can cause loss of vision when maintained for long periods. Extremely high pressures can cause blindness within days or even hours. As the pressure rises, the axons of the optic nerve are compressed where they leave the eyeball at the optic disc. This compression is believed to block axonal flow of cytoplasm from the retinal neuronal cell bodies into the optic nerve fibers leading to the brain. The result is lack of appropriate nutrition of the fibers, which eventually causes death of the involved fibers. It is possible that compression of the retinal artery, which enters the eyeball at the optic disc, also adds to the neuronal damage by reducing nutrition to the retina.
In most cases of glaucoma, the abnormally high pressure results from increased resistance to fluid outflow through the trabecular spaces into the canal of Schlemm at the iridocorneal junction. For instance, in acute eye inflammation, white blood cells and tissue debris can block these trabecular spaces and cause an acute increase in intraocular pressure. In chronic conditions, especially in older individuals, fibrous occlusion of the trabecular spaces appears to be the likely culprit.
Glaucoma can sometimes be treated by placing drops in the eye that contain a drug that diffuses into the eyeball and reduces the secretion or increases the absorption of aqueous humor. When drug therapy fails, operative techniques to open the spaces of the trabeculae or to make channels to allow fluid to flow directly from the fluid space of the eyeball into the subconjunctival space outside the eyeball can often effectively reduce the pressure.
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