# Range of accommodation in myopia

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?

• 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. Commented Jul 17, 2022 at 23:43
• "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? Commented Jul 18, 2022 at 0:15
• @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. Commented Jul 18, 2022 at 0:24
• 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. Commented Jul 18, 2022 at 2:03
• 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. Commented Jul 18, 2022 at 2:52

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.
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 $$25\,\rm cm$$.