Optics related math

Here's a page with maths related to diopters and glasses.

Diopters are inverse meters

Remember that 100cm = 1m.

$D={\frac {1}{meters}}$

conversely

$meters={\frac {1}{D}}$

Point of refraction

https://youtube/9z2jjT_Gm7o

$s=distance\ to\ object$ (meters)

$s'=distance\ to\ point\ of\ refraction$ (meters)

$f=focal\ length\ of\ lens$ (meters)

$P=power\ of\ lens$ (diopters)

${\frac {1}{f}}=({\frac {1}{s}})+({\frac {1}{s'}})$

${\frac {1}{f}}=P$

Visual acuity equation

$({\frac {font\ height}{distance\ to\ sign}})({\frac {180}{60pi}})=arcminutes=a$

Note: 5Arcminutes = 20/20

Set up proportion: ${\frac {a}{({\frac {20}{x}})}}={\frac {5}{({\frac {20}{20}})}}$

Visual acuity (mm/metres)

${\frac {font\ height(mm)}{distance\ to\ sign(m)}}\times 13.75=denominator\times of{\frac {20}{x}}$

Visual acuity (in/feet)

${\frac {font\ height(in)}{distance\ to\ sign(ft.)}}\times 1146=denominator\times of{\frac {20}{x}}$

With text that we are familiar the brain may clear up that text more than our vision actually operates at.

Average axial length accomodation/rate of change

$typical\ emmetropic\ eye=25mm=25,000\ microns$

$change\ in\ axial\ length\ of\ 1mm=3D$

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