Near point

In visual perception, the near point is the closest point at which an object can be placed and still form a focused image on the retina, within the eye's accommodation range. The other limit to the eye's accommodation range is the far point.

A normal eye is considered to have a near point at about 11 cm (4.3 in) for a thirty year old.^[1] The near point is highly age dependent (see accommodation). A person with hyperopia or presbyopia would have a near point that is farther than normal.

Sometimes, near point is given in diopters (see Presbyopia § Mechanism), which refers to the inverse of the distance. For example a normal eye would have a near point of ${\frac {1}{11\ {\text{cm}}}}=9\ {\text{diopters}}$ .

Vision correction[]

A person with hyperopia has a near point further than comfortable, (i.e. 25 cm) $NP > 25 cm$ , and hence is unable to bring an object 25 cm away into sharp focus. A corrective lens can be used to correct hyperopia by imaging an object at distance $D = 25 cm$ onto a virtual image at the patient's near point.^[2] From the thin lens formula, the required lens will have optical power $P$ given by^[3]^[4]

$P\approx {\frac {1}{D}}-{\frac {1}{\mathit {NP}}}$ .

The calculation can be further improved by taking into account the distance between the spectacle lens and the human eye, which is usually about 1.5 cm:

$P={\frac {1}{D-0.015\;{\text{m}}}}-{\frac {1}{{\mathit {NP}}-0.015\;{\text{m}}}}$ .

For example, if a person has $NP = 1 m$ , then the optical power needed is $P = +3.24 diopters$ where one diopter is the reciprocal of one meter.

References[]

^ Duane, Alexander (1922). "Studies in Monocular and Binocular Accommodation with their Clinical Applications". American Journal of Ophthalmology. 5 (11): 865–877. doi:10.1016/s0002-9394(22)90793-7.
^ Keeports, David (2016). "Fix your own vision". The Physics Teacher. 54 (6): 375–376. doi:10.1119/1.4961187. ISSN 0031-921X.
^ "Vision Correction | Physics". courses.lumenlearning.com. Retrieved 2019-12-05.
^ Goyal, Ashish; Bopardikar, Ajit; Tiwari, Vijay Narayan (2018). "Estimation of Spherical Refractive Errors Using Virtual Reality Headset". 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). Honolulu, HI: IEEE: 4976. doi:10.1109/EMBC.2018.8513209. ISBN 978-1-5386-3646-6.

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[Duane-1] Duane, Alexander (1922). "Studies in Monocular and Binocular Accommodation with their Clinical Applications". American Journal of Ophthalmology. 5 (11): 865–877. doi:10.1016/s0002-9394(22)90793-7.

[2] Keeports, David (2016). "Fix your own vision". The Physics Teacher. 54 (6): 375–376. doi:10.1119/1.4961187. ISSN 0031-921X.

[3] "Vision Correction | Physics". courses.lumenlearning.com. Retrieved 2019-12-05.

[4] Goyal, Ashish; Bopardikar, Ajit; Tiwari, Vijay Narayan (2018). "Estimation of Spherical Refractive Errors Using Virtual Reality Headset". 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). Honolulu, HI: IEEE: 4976. doi:10.1109/EMBC.2018.8513209. ISBN 978-1-5386-3646-6.

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