The Eye

The Anatomy of the Eye

The human eye is a complex anatomical device that remarkably demonstrates the arhitectural wonders of the human body. Like a camera, the eye is able to refract light and produce a focused image that can stimulate neural responses and enable the ability to see. In Lesson 6, we will focus on the physics of sight. We will use our understanding of refraction and image formation to understand the means by which the human eye produces images of distant and near-by objects. Additionally, we will investigate some of the common vision problems which plague humans and the customary solutions to those problems. As we proceed through Lesson 6, we will apply our understanding of refraction and lenses to the physics of sight.

The eye is essentially an opaque eyeball filled with a water-like fluid. In the front of the eyeball is a transparent opening known as the cornea. The cornea is a thin membrane which has an index of refraction of approximately 1.38. The cornea has the dual purpose of protecting the eye and refracting light as it enters the eye. After light passes through the cornea, a portion of it passes through an opening known as the pupil. Rather than being an actual part of the eye's anatomy, the pupil is merely an opening. The pupil is the black portion in the middle of the eyeball. It's black appearance is attributed to the fact that the light which the pupil allows to enter the eye is absorbed on the retina (and elsewhere) and does not exit the eye. Thus, as you sight at another person's pupil opening, no light is exiting their pupil and coming to your eye; subsequently, the pupil appears black.

Like the aperture of a camera, the size of the pupil opening can be adjusted by the dilation of the iris. The iris is the colored part of the eye - being blue for some people and brown for others (and so forth); it is a diaphragm which is capable of stretching and reducing the size of the opening. In bright-light situations, the iris is dilated to reduce the size of the pupil and limit the amount of light which enters the eye; and in dim-light situations, the iris adjusts its size so as to maximize the size of the pupil and increase the amount of light which enters the eye. Light which passes through the pupil opening, will enter the crystalline lens. The crystalline lens is made of a fibrous, jelly-like material which has an index of refraction of 1.44. Unlike the lens on a camera, the lens of the eye is able to change its shape and thus serves to fine-tune the vision process. The lens is attached to the ciliary muscles. These muscles relax and contract in order to change the shape of the lens. By carefully adjusting the lenses shape, the ciliary muscles asist the eye in the critical task of producing an image on the back of the eyeball.

The inner surface of the eye is known as the retina. The retina contains the rods and cones which serve the task of detecting the intensity and the frequency of the incoming light. An adult eye is typically equipped with 120 million rods which detect the intensity of light and 6 million cones which detect the frequency of light. These rods and cones send nerve impulses to the brain. The nerve impulses travel through a network of nerve cells; there are as many as one-million neural pathways from the rods and cones to the brain. This network                                                                 of nerve cells is bundled together to form the optic nerve on the very back of the eyeball.

Each part of the eye plays a distinct part in enabling humans to see. The ultimate goal of such an anatomy is to allow humans to focus images on the back of the retina.

Image Formation and Detection

Earlier in Lesson 6, we learned that the eye consists of a cornea (thin outer membrane), a lens attached to ciliary muscles, and a retina (inner surface equipped with nerve cells). These four parts of the eye are the most instrumental in the task of producing images which are discernible by the brain. In order to facilitate the ability to see, each part must enable the eye to refract light so that is produces an image on the retina.

It is a surprise to most people to find out that the lens of the eye is not where the refraction of incoming light rays takes place. Most of the refraction occurs at the cornea. The cornea is the outer membrane of the eyeball which has an index of refraction of 1.38. The index of refraction of the cornea is significantly greater than the index of refraction of the surrounding air. This difference in optical density between the air the corneal material combined with the fact that the cornea has the shape of a converging lens is what explains the ability of the cornea to do most of the refracting of incoming light rays. The crystalline lens is able to alter its shape due to the action of the ciliary muscles. This serves to induce small alterations in the amount of corneal bulge as well as to fine-tune some of the additional refraction which occurs as light passes through the lens material.

The bulging shape of the cornea causes it to refract light in a manner to similar to a double convex lens. The focal length of the cornea-lens system varies with the amount of contraction (or relaxation) of the ciliary muscles and the resulting shape of the lens. In general, the focal length is approximately 1.8 cm, give or take a millimeter. As learned in our discussion of convex lenses in Lesson 5, the image location, size, orientation, and type is dependent upon the location of the object relative to the focal point and the 2F point of a lens system. Since the object is typically located at a point in space more than 2-focal lengths from the"lens," the image will be located somewhere between the focal point of the "lens"
and the 2F point. The image will be inverted, reduced in size, and real. Quite conveniently, the cornea-lens system produces an image of an object on the retinal surface; the process by which this occurs is known as accomodation and will be discussed in more detail in the next part of Lesson 6. Fortunately, the image is a real image - formed by the actual convergence of light rays at a point in space. Vision is dependent upon the stimulation of nerve impusles by an incoming light photon;only real images would be capable of producing such a stimulation. Finally, the reduction in the size of the image allows the entire image to "fit" on the retina. The fact that the image is inverted poses no problem; our brain has become quite accustomed to this and properly interprets the signal as originating from a right-side-up object.

The use of the lens equation and magnification equation can provide an idea of the quantitative relationship between the object distance, image distance and focal length. For now we will assume that the cornea-lens system has a focal length of 1.80 cm (0.0180 m). We will attempt to determine the image size and image location of a 6-foot tall man (ho=1.83 m) who is standing a distance of approximately 10 feet away (do=3 meters).

The Wonder of Accomodation

While the entire surface of the retina contains nerve cells, there is a small portion with a diameter of approximately 0.25 mm where the concentration of rods and cones is greatest. This region, known as the fovea centralis, is the optimal location for the formation of the image. The eye typically rotates in its socket in order to focus images of objects at this location. The distance from the cornea (where the light undergoes most of its refraction) to the central portion of the fovea on the retina is approximately 1.7 cm. Light entering the cornea must produce an image with an image distance of 1.7 cm. Unlike a camera, which has the ability to change the distance between the film (the detector) and the lens, the distance between the retina (the detector) and the cornea (the "refractor") is
fixed. The image distance is unchangeable. Subsequently, the eye must be able to alter the focal length in order to focus images of both nearby and far away objects upon the retinal surface. As the object distance changes, the focal length must be changed in order to keep the image distance constant.

The ability of the eye to adjust its focal length is known as accomodation. Since a nearby object (small dobject) is typically focused at a further distance (large dimage), the eye accomodates by assuming a
lens shape that has a shorter focal length. This reduction in focal length will cause more refraction of light and serve to bring the image back closer to the cornea/lens system and upon the retinal surface. So for nearby objects, the ciliary muscles contract and squeeze the lens
into a more convex shape. This increase in the curvature of the lens corresponds to a shorter focal length. On the other hand, a distant object (large dobject) is typically focused at a closer distance (small dimage). The eye accomodates by assuming a lens shape that has a longer focal length. So for distant objects the ciliary muscles relax and the lens returns to a flatter shape. This decrease in the curvature of the lens corresponds to a longer focal length. The data table below demonstrates how a changing focal length would be required to maintain a changing focal length would be required to maintain a constant image distance of 1.70 cm.

The ability of the eye to accomodate is automatic. Furthermore, it occurs instantaneously. Focus on a far away object and quickly turn your attention to a nearby object; observe that there is no noticeable delay in the ability of the eye to bring the nearby object into focus. Accomodation is a remarkable feat! The power of a lens is measured by opticians in a unit known as a diopter. A diopter is equal to the reciprocal of the focal length. diopters = 1/(focal length)

A lens system with a focal length of 1.7 cm (0.017 m) is a 59-diopter lens. A lens system with a focal length of 1.59 cm is a 63-diopter lens. A healthy eye is able to bring both distant objects and nearby objects into focus without the need for
corrective lenses. That is, the healthy eye is able to assume both a small and a large focal length; it would have the ability to view objects with a large variation in distance. The maximum variation in the power of the eye is called the Power of Accomodation. If an eye has the ability to assume a focal length of 1.70 cm (59-diopters) to view objects many miles away as well as the ability to assume a 1.59 cm focal length to view an object 0.25-meters away (63-diopters), then its Power of Accomodation would be measured as 4 diopters (63 diopters - 59 diopters).

The healthy eye of a young adult has a Power of Accomodation of approximately 4 diopters. As a person grows older, the Power of Accomodation typically decreases as a person becomes less able to view nearby objects. This failure to view nearby objects leads to the need for corrective lenses.