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[[File:Math guy with glasses.gif|right]]
{{gif fixer|[[File:Math guy with glasses.gif]]|right}}
Here's a page with maths related to diopters and glasses.
Here's a page with maths related to diopters and glasses.


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A diverging lens behaves in a similar way, but for distant objects - the light rays incident from the source object are refracted outwards so that they are diverging even faster. Again, a virtual focus is said to form behind the lens. The thin lens equation still works as long as you use negative numbers to describe both the (virtual) image location and the focal length.
A diverging lens behaves in a similar way, but for distant objects - the light rays incident from the source object are refracted outwards so that they are diverging even faster. Again, a virtual focus is said to form behind the lens. The thin lens equation still works as long as you use negative numbers to describe both the (virtual) image location and the focal length.


The corrective lens for [[myopia]] is a diverging lens. It works by forming a virtual image of distant objects, and it is this virtual image that the near-sighted eye is able to focus on.
The corrective lens for [[myopia]] is a diverging lens. It works by forming a virtual image of distant objects, and it is this virtual image that the near-sighted eye is able to focus on. (You can also choose to think of it as lens in series with your eye, forming a compound lens with lower power and therefore a longer focal length.)
 
===Diopters are inverse meters===
===Diopters are inverse meters===


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Remember that 100cm = 1m.
Remember that 100cm = 1m.


<math>D = \frac{1}{meters}</math>
<math>D = \frac{1}{ \text{meters} }</math>


conversely
conversely


<math>meters = \frac{1}{D}</math>
<math> \text{meters} = \frac{1}{D}</math>


==Calculating correction==
==Calculating correction==
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==Visual acuity equation==
==Visual acuity==
<math>(\frac{font\ height}{distance\ to\ sign})(\frac{180}{pi}) \times 60 = arcminutes = a</math>
[[File:TrigonometryTriangle.svg|right|TrigonometryTriangle]]
 
A reminder about some trigonometry / geometry
# <math>\tan(A) = \frac{a}{b}</math>
#* so for fixed angle, 'a' is proportional to 'b'
# for very small angles (expressed in radians), <math>\tan(A) \approx A</math>
#* so at small angles, 'a' is proportional to 'A'
# <math>1 \text{ radian} = \frac{180}{\pi} \text{ degrees} = \frac{60 \times 180}{\pi} \text{ arc-minutes} </math>
 
Acuity is a measure of the ability to resolve small details, defined by the "minimum angle of resolution". Normal vision ("20/20", or 1.0) is the ability to resolve features subtending 1 minute of arc. In order to have a bigger-is-better score, the reciprocal of the angle is usually used:
 
<math> \text{Acuity} = 1/A = \frac{pi}{60 \times 180} \times \frac{b}{a} = 0.00029 \times \frac{b}{a}</math>


Note: 5Arcminutes = 20/20
An alternative representation of acuity is "logMAR" ("log<sub>10</sub> Minimum Angle of Resolution"). This has a bigger-is-worse direction.
* 0.0 corresponds to "20/20" (1.0 or 1 arc-minute)
* 1.0 is "20/200" (0.1 or 10 arc-minutes)
* -0.3 is "20/10" (2.0 or 0.5 arc-minutes)


Set up proportion: <math>\frac{a}{(\frac{20}{x})} = \frac{5}{(\frac{20}{20})}</math>
On a [[Snellen chart]] the letters are defined on a 5x5 grid: the detail to be resolved to distinguish between characters is one pixel of that grid.
Here 'b' is the distance to the chart (eg 6m) and 'a' is the height of the letters. It's not critical that the eye is at the bottom or top of a row of letters - as long as the angles remain small, the numerical error is insignificant.


===Visual acuity (mm/metres)===
Acuity is reported in the form "distance/letter-row", such as "20/40", etc.
<math>\frac{font\ height (mm)}{distance\ to\ sign(m)} \times 13.75 = denominator \times of \frac{20}{x}</math>


===Visual acuity (in/feet)===
<math> \text{Acuity} = 5 \times 0.00029 \times \frac{ \text{distance to chart} }{ \text{letter height} }
<math>\frac{font\ height(in)}{distance\ to\ sign(ft.)} \times 1146 = denominator \times of \frac{20}{x}</math>
= \frac{ \text{distance to chart} }{690 \times \text{letter height} } </math>
<ref>{{cite jake|https://endmyopia.org/use-math-to-turn-any-text-into-your-own-impromptu-eyechart/}}</ref>


With text that we are familiar with, the brain may clear up that text more than our vision would actually allow.<ref>{{cite jake|https://endmyopia.org/use-math-to-turn-any-text-into-your-own-impromptu-eyechart/}}</ref>
Then, for example
* for the "6/12" line, we need <math>690 \times \text{height} = 12m \implies \text{height} = 12m / 690 = 1.73cm</math>
* for the "20/15" line, we need <math>690 \times \text{height} = 15ft \implies \text{height} = 15 * 12 / 690 = 0.26 \text{inch}</math>
 
The denominator can be interpreted as the distance at which the letters subtend 5 minutes of arc.


==Average axial length accomodation/rate of change==
==Average axial length accomodation/rate of change==
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* [[Vertex distance]]
* [[Vertex distance]]
* [[Wikipedia:Vertex_distance|Vertex distance formula (also for astigmatism)]]
* [[Wikipedia:Vertex_distance|Vertex distance formula (also for astigmatism)]]
==See Also==
[https://wiki.endmyopia.org/wiki/Guide:Reducing_differentials#First_differentials Guide:Reducing differentials > First differentials]


==References==
==References==
{{reflist}}
{{reflist}}
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