Here's a page with maths related to diopters and glasses.
You don't really need to know any of this stuff to improve your eyesight, but it's good to know for deeper understanding
Diopters are inverse meters
See Also Diopters
Remember that 100cm = 1m.
D
=
1
m
e
t
e
r
s
{\displaystyle D={\frac {1}{meters}}}
conversely
m
e
t
e
r
s
=
1
D
{\displaystyle meters={\frac {1}{D}}}
Point of refraction
See also Refraction
s
=
d
i
s
t
a
n
c
e
t
o
o
b
j
e
c
t
{\displaystyle s=distance\ to\ object}
s
′
=
d
i
s
t
a
n
c
e
t
o
p
o
i
n
t
o
f
r
e
f
r
a
c
t
i
o
n
{\displaystyle s'=distance\ to\ point\ of\ refraction}
f
=
f
o
c
a
l
l
e
n
g
t
h
o
f
l
e
n
s
{\displaystyle f=focal\ length\ of\ lens}
P
=
p
o
w
e
r
o
f
l
e
n
s
{\displaystyle P=power\ of\ lens}
1
f
=
(
1
s
)
+
(
1
s
′
)
{\displaystyle {\frac {1}{f}}=({\frac {1}{s}})+({\frac {1}{s'}})}
1
f
=
P
{\displaystyle {\frac {1}{f}}=P}
Visual acuity equation
(
f
o
n
t
h
e
i
g
h
t
d
i
s
t
a
n
c
e
t
o
s
i
g
n
)
(
180
60
p
i
)
=
a
r
c
m
i
n
u
t
e
s
=
a
{\displaystyle ({\frac {font\ height}{distance\ to\ sign}})({\frac {180}{60pi}})=arcminutes=a}
Note: 5Arcminutes = 20/20
Set up proportion:
a
(
20
x
)
=
5
(
20
20
)
{\displaystyle {\frac {a}{({\frac {20}{x}})}}={\frac {5}{({\frac {20}{20}})}}}
Visual acuity (mm/metres)
f
o
n
t
h
e
i
g
h
t
(
m
m
)
d
i
s
t
a
n
c
e
t
o
s
i
g
n
(
m
)
×
13.75
=
d
e
n
o
m
i
n
a
t
o
r
×
o
f
20
x
{\displaystyle {\frac {font\ height(mm)}{distance\ to\ sign(m)}}\times 13.75=denominator\times of{\frac {20}{x}}}
Visual acuity (in/feet)
f
o
n
t
h
e
i
g
h
t
(
i
n
)
d
i
s
t
a
n
c
e
t
o
s
i
g
n
(
f
t
.
)
×
1146
=
d
e
n
o
m
i
n
a
t
o
r
×
o
f
20
x
{\displaystyle {\frac {font\ height(in)}{distance\ to\ sign(ft.)}}\times 1146=denominator\times of{\frac {20}{x}}}
With text that we are familiar the brain may clear up that text more than our vision actually operates at.[1]
Average axial length accomodation/rate of change
t
y
p
i
c
a
l
e
m
m
e
t
r
o
p
i
c
e
y
e
=
25
m
m
=
25
,
000
m
i
c
r
o
n
s
{\displaystyle typical\ emmetropic\ eye=25mm=25,000\ microns}
c
h
a
n
g
e
i
n
a
x
i
a
l
l
e
n
g
t
h
o
f
1
m
m
=
3
D
{\displaystyle change\ in\ axial\ length\ of\ 1mm=3D}
If someone with typical eyes wanted to adapt say 20/20 to .25 less
normalized within 3-4 months
would need to decrease axial length 0.083mm
about 0.92microns/day - 0.69microns/day average
Credit: Mark Podowski
