Schematic Eyes

The major challenges to understanding the optics of the human eye lie in the complexities and “imperfections” of some of the eye’s optical elements. Simplifications and approximations make models easier to understand but limit their ability to explain all the subtleties of the eye’s optical system. As an example, the anterior surface of the cornea is frequently assumed to be spherical, but the actual anterior surface tends to flatten toward the limbus. Also, the center of the crystalline lens is usually decentered with respect to the cornea and the visual axis of the eye.

Many mathematical models of the eye’s optical system are based on careful anatomical measurements and approximations. The model developed by Gullstrand (Fig 3-1, Table 3-1), a Swedish professor of ophthalmology, so closely approximated the human eye that he was awarded a Nobel Prize in 1911. Although very useful, this model is cumber-some for certain clinical calculations and is often simplified further.

Because the principal points of the cornea and lens are fairly close to each other, a single intermediate point can substitute for them. In a similar fashion, the nodal points of the cornea and lens can be combined into a single nodal point located 17.0 mm in front of the retina. Thus, we can treat the eye as if it were a single refracting element, an ideal spherical surface separating 2 media of different refractive indices: 1.000 for air and 1.333 for the eye (Fig 3-2). This simplified model is known as the reduced schematic eye.

Figure 3-1 Optical constants of the Gullstrand eye. All values in millimeters. A, Refractive indices of the media and positions of the refracting surfaces. B, Positions of the cardinal points, which are used for optical calculations.

(Illustration by C. H. Wooley.)

Using this reduced schematic eye, we can calculate the retinal image size of an object in space (such as a Snellen letter). This calculation utilizes the simplified nodal point, through which light rays entering or leaving the eye pass undeviated. The geometric principle of similar triangles can be used for the calculation of retinal image size if the following information is given: (1) the actual height of a Snellen letter on the eye chart, (2) the distance from the eye chart to the eye, and (3) the distance from the nodal point to the retina. The formula for this calculation is as follows:

Table 3-1 The Schematic Eye

Figure 3-2 Dimensions of the reduced schematic eye, defined by the anterior corneal surface (P), the simplified nodal point of the eye (N), and the fovea (F′). The distance from the simplified nodal point to the fovea is 17.0 mm, and the distance from the anterior corneal surface to the nodal point is 5.6 mm. The refractive index for air is taken to be 1.000, and the simplified refractive index for the eye (n′) is 1.333. The refractive power of this reduced schematic eye is 60.0 D, with its principal plane at the front surface of the cornea.

(Illustration by C. H. Wooley.)

Although the distance from the eye chart to the nodal point should be measured, it is much easier to measure the distance to the surface of the cornea. The difference between these measurements is 5.6 mm, which is usually insignificant. For example, if the distance between the nodal point and the retina is 17.0 mm, the distance between the eye chart and the eye is 20 ft (6000 mm), and the height of a Snellen letter is 60 mm, then the resulting image size on the retina is 0.17 mm.

• Katz M, Kruger PB. The human eye as an optical system. In: Tasman W, Jaeger EA, eds. Duane’s Clinical Ophthalmology [CD-ROM]. Vol 1. Philadelphia: Lippincott Williams & Wilkins; 2013:chap 33.

Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.