## Eye Math

## Size of a 20/20 letter on the eye chart.

The minimum separation between two lines that an average person can see has been measured as an angle of one minute of arc. (1 min is 1/60 of a degree)

Using this strategy a letter on a vision chart is made to measure the smallest space the subject can distinguish. For a 20/20 letter there are three bars and two spaces making the total letter height 5 min with 1 min between the lines.

To figure out how tall this needs to be at a testing distance of 20 feet we can make the following calculations.

**Using the Reduced Schematic Eye**

This is a simplified model of the optics of the eye, useful for calculating both object and retinal image size.

We will calculate the letter height, L, at distance, D, for both 20 feet and 6 meters.

To simplify the numbers we can do the calculation at 1 degree then divide by 12 to get 5 min.

** The Rest of the Letters**

A 20/40 letter is twice the height of a 20/20 letter and a 20/200 letter is 10 times that.

## Calculate Retinal Image Size

Looking the other direction the size of the 20/20 letter on the retina can be found by the above method or by similar triangles.

One can then estimate the spacing of the retinal photoreceptors so they are able to distinguish line-space-line. Minimum spacing would be one receptor to sense the first line, a second to sense the space and a third to sense the second line. Studies measuring the size of receptors show good agreement with this spacing and suggest the theoretically best vision would be about 20/10.