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

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

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

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

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 P = power\ of\ lens} (diopters)

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

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{1}{f} = P}

Visual acuity equation

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{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)

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

Visual acuity (in/feet)

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{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

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

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 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