Modeling the Optics of the Eye and Corrective Lenses

Manushi Shah and John Noe, Laser Teaching Center, Physics and Astronomy

Everyone is familiar with corrective lenses and most people will need them at some time in their life. Glass lenses have been used to correct vision for nearly 10 centuries. Eyeglasses became widely used after the invention of printing in 1440, and Benjamin Franklin invented bifocal eyeglasses in 1784. Glass and hard plastic contact lenses date from 1887 and 1948 respectively. Contact lenses now come in a variety of soft materials, can be worn for extended periods and can correct for a wide variety of visual defects. Visual defects can now even be corrected permanently by laser eye surgery, which reshapes the cornea.

The focusing power of the eye or corrective lenses is measured in diopters, the inverse of the focal length measured in meters. About two-thirds of the approximately 50 diopter strength of the normal eye comes from the spherical entrance surface (cornea), while one-third comes from the crystalline lens. A far-sighted person needs additional focusing power (a convex or converging lens) to move the focal point of the rays from behind the retina onto its surface. A near-sighted person needs a concave or diverging corrective lens. Corrective lenses typically have strengths from -5 to +5 diopters, where the sign indicates diverging or converging.

The goal of this project is to model the optics of the eye and corrective lenses using a commercial ray-tracing program, BEAM2 [1]. The program is easy to use and learn. It is controlled by two tables: the optics table describes the refractive surfaces and the ray-table describes the rays that pass through them. As a first step, a normal eye was modeled as a ball of water (n = 1.33) with a convex lens of a slightly higher index (n = 1.5) within it. It will be straightforward to extend this model to include eye-glasses, contact lenses or even laser surgery. The realistic models created with this program should help future students gain a better and more quantitative understanding of the optics of the eye.

[1] Stellar Software, Berkeley, CA. http://www.stellarsoftware.com