Calc Size of 20/20 Letter
Size of a 20/20 letter on the eye chart.
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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.
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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. It is explained in more detail by clicking on the link.
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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.
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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.