A Very Much Simplified Model Eye
We now have in hand the tools to illustrate the correction of simple axial refractive errors, which arise from a mismatch between the optical power of the anterior segment (cornea and crystalline lens) and the axial length of the eye.
Suppose that all the refracting power of the eye is concentrated at a single plane, at the apex of the cornea, and assume the typical axial length of 24.0 mm. If this ultra-simplified model eye is to focus light from distant objects on the retina (Figure I-11A)—the power at the corneal apex must be given by the vergence equation: 0 + P = 1.33/0.024 m = 55.42 D. [The actual total nominal power of the human eye is in fact about 60 D, so our simplistic model is off by only about 10%.]
Now suppose that our eye has the standard anterior segment with optical power 55.42 D but is 1.0 mm longer than normal—so the axial length is 25.0 mm. In such an eye, which is said to be myopic, light from a distant point source comes to a focus where the retina “should have been” (Figure I-11B); then the rays cross and continue for another millimeter before they form an (annoying) blur-circle on the retina. To correct the refractive error, we must shift the image location 1.0 mm toward the back of the eye. This can be done, say, with a concave (diverging, “minus” power) contact lens of power P placed adjacent to the corneal apex according to the vergence equation: 0 + (P + 55.42 D) = 1.33/.025 D = +53.20 D. Thus, the power of the required contact lens is P = 53.20 D – 55.42 D = –2.22 D. [In a more precise calculation, the correction would be about –3 D for each millimeter of excess axial length.]
Figure I-11 The position of light rays focusing. A, The normal eye. B, A myopic eye. C, A hyperopic eye.
(Illustration developed by Scott E. Brodie, MD.)
Similarly, if the axial length of our ultra-simplified model eye were reduced by 1.0 mm, distant objects would form an image behind the retina (Figure I-11C). Such an eye is hyperopic. The required contact lens power would be given by the vergence equation: 0 + (P + 55.42 D] = 1.33/0.023 m = +57.83 D, or P = +57.83 D – 55.42 D = +2.41 D, a convex “plus” lens.
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.