Optics related math

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

Remember that 100cm = 1m.

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

conversely

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

Point of refraction

$s=distance\ to\ object$ (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