You are very much in need of some exact figures, primary sources, and a bit of logical clarification.
Eyeballs, like the earth itself, are not a perfect sphere; they are both flattened at the poles and fat around the equator. With the human eyeball ( I think) it is the axial length that is noticeably longer than other radii. Consult Oyster's textbook " Human Eye; it's structure and function" for exact figures. 24 mm. Diameter is often used. I, being a biologist, recognize these figures as being averages representing a spread of natural variation in the eye, in vivo, and for ease of calculation I just round up to a sphere of perfect 1" diameter, or 25.4 mm. and 12.7 mm. radius.
And some actual eyeball measurement data include the sclera which probably should be excluded considering our interest in the distance to the image surface.
Some definitions of diopters give it as the reciprocal of the focal length of a lens, which for simple thin lenses would probably be 1/f = 1/id + 1/od . It might be safe to assume that this is a thick lens system?
But we must make note that the image surface, the retina, is in contact with the vitreous humor. So, even if we "fudge it a bit" using the above thin lens formula, we should probably recognize that the intended image surface is some 16 mm. away from the final refractive surface.
So, using the thin lens approximation, id should be = 16 mm. and 1/0.016 = 62.5 .
For the far point of accommodation, a tricky measurement to guess, but depending upon light levels and depth of field and acceptable circle of confusion, generally agreed upon to be 1 meters, or 3 meters, or 5 meters. Obviously this is an age and disease related variable and the lens at this point is focused to infinity ( though focused to a distance of 1 or 3 or 5 meters, any object points beyond that distance, out to infinity, or the horizon, are within the depth of field range and circle of confusion parameters for "acceptable focus").
There is some terminology and equations about "Hyperfocal distance" but I forget them right now. See Davson's " Physiology of the Eye" for better instruction.
62.5 + (1/1) = 63.5 D , for the far point of accommodation. For distances of 3 or 5 meters, this value reduces to about 62.8 and 62.7 D.
For a near point of 12.5 cm, or 0.125 m., the dioptric power of the system is closer to 70.5 D.
Smith and Atchison circa 2000, have a book that is nothing but professional theoretical eye models. I often use a Navarro et. al. JOSA paper from 1985. Gullstrand got the Nobel for his work, back in the 19-oughts or 1910s, I think? Oyster circa 2000 and Hugh Davson circa 1980s "Physiology of the Eye" are also essential textbooks. LeGrand is an often used theoretical model eye, circa 1950s, I think.
Interesting attempts to reproduce functional models of the optics of the human eye include G.H. Gliddon's 1929 attempt, and Don Schultz's 1947 attempt. Both suffered from inappropriate lens materials. The index of refraction for the optical elements of the human eye are much lower than those regularly used in lens design and manufacture. ( Up until WWI, America was a scientific backwater, with no scientific glass production of their own. Most American "innovation" up to this point had been of the industrial, commercial, immediately lucrative variety.).
Now, with modern materials, a 1:1 scale model of the human eye might be attempted. Couple with that the increasing interest in curved focal plane arrays ( beginning with NASA and telescope enthusiasts) and the increasing pixel counts in image sensors over these past three decades and you have a recipe for some very fine cameras and very fine experimental realizations of theoretical, human-eye-inspired models.
Somewhere in my notes is buried the reference to Oyster, wherein he ascribes some 40 D of power to the air-cornea interface, and 20 diopters of power to the lens-aqueous interface. With additional accommodative power between 0 and + 15 the lens can turn the system from about 60 diopters to 75 diopters.
Osterberg retinal cell count of 1935 put the human eye ( estimate from subsample multiplication) at 120 million rod cells and 6 million cone cells. Subsequent work in the 1990s utilized some computer help for more accurate subsampling, and curio et.. al. put photoreceptor counts at about 90 million for rod cells and 4 million cone cells.
My figure of "about 16 mm." for lens to retina distance, comes from a 0.55 mm. thick cornea, approximately 3 mm. aqueous humor, approximately 4 mm. lens thickness and my "round assumption", of 25.4 mm diameter for the human eyeball, image space. 25.4 - 7.55 = 17.85.
OK. I ain't perfect. You redo the math if you want to. I used mostly Navarro et. al.s numbers 1985. But the human optical system has a lot of aspherical elements and is a badly tilted and decentered system. And the optical axis and the visual axis do not coincide. And "Meyer's Approximations" are really just something I invented to make the math easy.
