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Here's what I understand about accommodation of the eye and correcting myopia with a diverging lens. (Source material)

An ideal eye can accommodate and focus any object that is farther to the eye than its near point. For the sake of argument, let the near point be $25$cm. A myopic eye has trouble focusing objects that are farther than a finite 'far point'. In an ideal vision, far point is at infinity. Say the far point of a person with myopia is $50$cm.

Per the textbook argument, the function of a concave lens to correct for myopia is to focus an object at infinity (the ideal far point) at the actual far point ($50$cm here) because that's the farthest the unaided eye can focus. It then follows that a concave lens of focal length $-50$cm is needed. It is equal to $-2.0$D, which is quite common for prescription glasses.

They seem to imply that this correction changes the range of accommodation back to the ideal range ($25$cm to infinity). But that's not true? If the object distance is $45$cm, the image is formed by the concave lens at $23.7$cm. In fact it seems the range of accommodation is only $50$cm to infinity.

Is this correct? I wear glasses with $-2.0$D power but I don't notice that my near point has moved farther away. What am I missing in my analysis?

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  • $\begingroup$ Note that the near point of short-sighted eye are shorter than $25$ cm. When you'll have old sight at the future time, you need to wear progress/bifocal lens (less concave in the lower half of the lens) in order to have better vision for near objects. $\endgroup$ Commented Jul 17, 2022 at 23:43
  • $\begingroup$ "I don't notice that my near point has moved farther away." Are you saying that the closest distance you can maintain focus is identical whether your lenses are on or off? $\endgroup$
    – BowlOfRed
    Commented Jul 18, 2022 at 0:15
  • $\begingroup$ @BowlOfRed I've not tested the nearest point, but I can see objects between 25 cm and 50 cm with or without my glasses equally well. My main question is if the calculation I outlined above has any crucial assumptions or caveats. $\endgroup$
    – Aravind
    Commented Jul 18, 2022 at 0:24
  • $\begingroup$ You need to talk to an eye doctor to answer this question. And I note that -2 diopters is moderate. I had LASIK when my vision in contact lenses was -8.5 diopters. Since the correction has to be higher when the lens is farther away from the cornea, I'm sure that my glasses were in the range of -10.5. I'm sure that qualifies as legally blind without correction. $\endgroup$ Commented Jul 18, 2022 at 2:03
  • $\begingroup$ I don't see any problems with your calculation. But it does suggest that your assumption about the near point being at 25cm may be incorrect. $\endgroup$
    – BowlOfRed
    Commented Jul 18, 2022 at 2:52

1 Answer 1

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When the topic of vision correction is introduced and the near point is defined it is often the case that students will tell you that their near point is much less than $25\,\rm cm$.
They will show you them looking at a piece of text with their eye much less than $25\,\rm cm$ away from it and saying that they can read the text.
What some will not tell you is that although they can read the text it is not in sharp focus and that they cannot maintain that reading position over a period of time.
The answers to the question Why am I able to see objects within 25 cm? explains this in more detail.

Adding a single focal length correcting lens for a short sighted person will make the positions of both the near and far points move further away from the eye.
Adding a diverging lens makes the eye lens system weaker and so rays are not deviated as much, thus moving an object away, so requiring less bending of the rays, allows the lens system to produce a sharp image on the retina.
Although it might appear that the near point has not changed that is not the case and the change in the position of the near point then requires a change in position of text relative to the eye, the use of either bifocal or varifocal lenses or indeed another pair of spectacles.

A short-sighted eye often has a near point which is less than $25\,\rm cm$ from the eye and so when the correcting lens is used the new near point is further from the eye and can be near to $25\,\rm cm$.

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