Geometric Optical Formula on Accommodation in Human Eye

Abstract

A geometric optical formula which describes the accommodation in the human eye within a framework of Gaussian optics is presented. In this formula, Kepler’s idea on accommodation, which has been disregarded in the traditional theory, is correctly revived and the power of accommodation is represented in the form of the sum of the contributions of Helmholtz’ and Kepler’s terms. It is shown that the cause of pseudoaccommodation in pseudophakia is reasonably explained by Kepler’s term alone, and the results of the numerical calculations on the power of accommodation in a normal eye are in good agreement with those obtained by Helmholtz and Gullstrand. Finally, we arrive at the surprising conclusion that the contributions of Helmholtz’ and Kepler’s terms to the power of accommodation in a normal human eye are approximately in the ratio of 2 to 1 or 3 to 1. This strongly claims a rivival of Kepler’s idea on accommodation.