# Derivation of the relationship between snellen rows and diopters

The results of converting between rows of a snellen chart and diopters is indicated in the tables at these two links: How to Convert Diopters to 20/20 Vision and Conversion Table for Distance Vision

But: What is the derivation of the relationship between rows of a snellen chart and diopters?

• I've searched a lot(I think so :) ) but I haven't found any derivation at least in the medical texts in only those in my reach ;) I believe this question still is good for Physics SE. Mar 3 '19 at 16:24
• Here's an incorrect derivation -- results in the correct sign but too small a value: Interpret "20/40 correction" to mean that when a lens of power d_lens is placed in front of the eye, objects at 12 m form an image at the same location (retina) as objects at 6 m would for the naked eye. Assume the ciliary muscles do not change the power of the naked eye, d_eye, when viewing objects at 6 m or 12 m. So we have the two equations: 1/6 + 1/v = d_eye; and 1/12 + 1/v = d_lens + d_eye; And solving them yields: d_lens = -1/12 = -0.08 Mar 5 '19 at 1:57