I have a friend who has just show me his medical prescription for hyperopia (farsightedness) correction and he needs glasses with 4,25 diopters for that, which seemed to be weird for me because I had learned, from the mirror equation, that the maximum correction possible for hyperopia is 4 diopters:

$$

frac{1}{f} = frac{1}{p} + frac{1}{p’}

$$

If we have $0.25m$ for the normal eye distant point and more than $0.25m$ for the farsighted eye distant point (negative sign, because it’s a virtual image), then we would have:

$$

frac{1}{f} = frac{1}{0.25} + frac{1}{p’} = 4 – frac{1}{|p’|} inquad ]0,4[, quadtext{since}quad |p’| geq 0.25m quadtext{and}quad p'<0

$$

I did some google search and find out that, indeed, hyperopia can reach values even greater, such as 20 diopters, but I can’t find pages where doctors explain that with equations or physics teachers explain how things really work in ophthalmology.

Either I am doing some terrible mistake, or doctors are doing some terrible mistake, or this equation just don’t apply to hyperopia at all… Which one is true?