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

See Also Diopters

See Also cm Measurement

Remember that 100cm = 1m.

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

conversely

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle meters = \frac{1}{D}}

Point of refraction

See also Refraction

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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

Converting from Glasses to Contact Lens Prescription or vice-versa

Vertex distance formula (also for astigmatism)