Relationship between axial length and chromatic refraction of the eye

A new mathematical expression is derived to provide an estimate, alpha x, of the axial length of the human schematic eye. Approximations in the expression are made after considering effects in the Gullstrand-Emsley schematic eye. Parameters required to solve the expression are, for two wavelengths, the refractive indices of the humours, the focal power of the cornea and refractive errors in two states of accommodation. Unlike recognized optical methods, additional intraocular parameters are not required. For emmetropic variants of the Gullstrand-Emsley schematic eye with axial lengths between 19 and 27 mm, alpha x is within 0.06 to 0.26 mm of the actual value. Furthermore, alpha x is essentially independent of variations in the refractive indices of the crystalline lens. However, the estimate of alpha x is critically dependent on the accuracy of values assigned to the parameters. For that reason, the model is considered impractical for clinical application.