72 Physics of the Eye

The human eye is one of the most remarkable optical instruments found in nature. It continuously forms sharp images of objects over an enormous range of distances while allowing us to perceive fine detail, color, motion, and depth. Although many people require glasses or contact lenses to achieve ideal vision, the basic operation of the eye can be understood using the same principles of geometric optics developed in the previous chapters.

In this chapter we will examine how the eye forms images, why vision changes with age, and how the eye's optical properties are used in medicine and vision correction. Understanding the physics of the eye also provides the foundation for understanding cameras, microscopes, telescopes, and many modern medical imaging instruments.

Figure 72.1 illustrates the basic anatomy of the eye. The cornea and the crystalline lens together behave much like a single converging lens. Their job is to focus incoming light so that a sharp real image forms on the retina, the light-sensitive layer lining the back of the eye.

The retina contains millions of specialized photoreceptor cells that convert light into electrical signals. These signals are processed by retinal neurons before traveling through the optic nerve to the brain, where they are interpreted as the images we perceive.

The central portion of the retina, called the fovea, provides our highest visual acuity because it contains the greatest concentration of cone photoreceptors. This is why we naturally move our eyes so that objects of interest fall on the fovea. In contrast, the peripheral retina contains fewer cones and more rod photoreceptors, making it much better at detecting motion and dim light but less effective at distinguishing fine detail and color.

The eye is also remarkably adaptable to changes in brightness. The pupil, whose diameter is controlled by muscles in the iris, regulates the amount of light entering the eye. Together with biochemical changes inside the photoreceptors, this allows the visual system to function over an enormous range of light intensities—from dim starlight to bright sunlight.

Another important property governing image formation is the refractive index of the tissues through which light passes. Whenever light enters a material with a different refractive index, its speed changes and the light bends according to Snell's law.

Refractive Indices of the Eye

Table 72.1 lists the refractive indices of the major optical media in the eye. Notice that the largest change occurs when light passes from air into the cornea. Consequently, the cornea supplies most of the eye's focusing power, while the crystalline lens provides the fine adjustments needed to focus objects at different distances.

Although light passes through several transparent structures—including the cornea, aqueous humor, lens, and vitreous humor—the optical system can usually be modeled as a single thin converging lens. As shown in Figure 72.2, rays from each point on an object converge to corresponding points on the retina, producing a real, inverted image. The visual cortex in the brain processes this information so that objects appear upright.

Accommodation

For clear vision, the image must always form precisely on the retina. Because the distance from the lens to the retina remains essentially constant, the eye changes its focal length rather than changing the image distance. This process is called accommodation.

When viewing distant objects, incoming light rays are nearly parallel and require relatively little bending. The ciliary muscles relax, causing the lens to become flatter and reducing its optical power. When viewing nearby objects, the rays reaching the eye diverge more strongly, so the ciliary muscles contract and the lens becomes thicker and more curved, increasing its focusing power.

A healthy young adult can typically focus on objects from about [latex]25~\text{cm}[/latex] away to essentially infinity. The closest distance at which an object can be focused sharply is called the near point. As we age, the lens gradually stiffens, making accommodation increasingly difficult.

Modeling the Eye as a Thin Lens

Because the eye behaves approximately like a thin converging lens, we can analyze it using the same equations introduced earlier. Since the optical power of a lens is

the thin-lens equation becomes

The magnification is

For clear vision, the image distance [latex]d_i[/latex] must equal the distance from the eye's lens to the retina. Throughout this chapter, we will assume that a person with normal vision can focus on objects located between approximately [latex]25~\text{cm}[/latex] and infinity.