When teaching future physicians we propose them problems to solve. A popular kind of problems is devoted to precipitation of glasses or contact lenses for shortsighted eyes because myopia is nearer to students' practice. Though as I changed those problems a little to consider the case of hypermetropia I came to conclusion that this defect of vision could be corrected with lenses very restrictedly. Indeed, if we consider the best vision distance to be d = 0.25 m, then for focal power of the patient's eye 1/F more than +4 D the thin lense equation 1/F = 1/d - 1 /f could not be satisfied for any distance between the lense and an image (f), so that the laser correction is needed in this case. Is it right?
No, definitely not right, I’m afraid. The 4 diopters is not the only lens. It is the correction, the extra lens. Consider a person with perfect vision. They need no correction. Their correction is 0 diopters. The focal length is infinity. That is definitely not the focal length of their eyes!
Now, how to do it right? Eyes are not anything like thin lenses, so perhaps it is best to avoid the thin lens equation. Instead, consider that the prescription is the extra lens required to focus at infinity. That is to say, with the addition of the required prescription parallel rays will be brought to a focus at the retina. So, what additional lens would you need to focus at a finite conjugate? The lens that takes the object to collimated rays. In other words a lens with focal length equal to the finite conjugate.
So, any eye that can be well corrected to focus at infinity with some prescription, whether -6 diopters or +8, can then be focused at 0.25m by the addition of an additional 0.25 m focal length positive lens. (or any other distance you like)
Thank you, Dr. Albert for your answer. Indeed, ophtalmologists usually propose their patients to read a table of letters, from your answer I can guess that they do it to check ability of patient's eyes to be focused at infinity. Though I don't ask about our eyes' optical system: of course, they are thick lenses, to which the mentioned equation is inapplicable; our eye in norm has its own optical power, which is changed every time because of accomodation. That's well.
My question is about extra lenses. If we hear that somebody's sight is +2 D we understand that is about extra lenses used for correction, aren't we? As a patient needs glasses (contact lenses) for reading an ophtalmololist prescribes extra lenses believing that a book should be placed at the distance 25 cm from the patient's eyes, doesn't he/she? It means that even for sever prebyopia the maximal strength of extra lenses used for reading couldn't be more than +4D, isn't it?
Yes, I understood what you were saying. I was trying to explain that you are not thinking about it correctly. Whatever the prescription, that is the lens which brings infinity to focus on the retina. An additional lens (beyond the prescription) with a focal length of 25 cm would then bring an object at 25 cm into focus. This is a proof of existence, but, of course, if you can do it with two closely spaces lenses, you can just as easily do it with a single lens.
The reason your logic doesn’t work is because you are using the prescription lens and using it in the thin lens equation as if it were all by itself and the eye doesn‘t exist. That’s just the wrong approach.
Thank you, Doctor Albert.
"It's sad, so sad... It's so sad, sad situation.
And it's getting more and more absurd.." [1] : Why do oculists and physicists use different words?
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[1]. Elton John. "Sorry seems to be the hardest word".
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