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

$s=distancetoobject$ (meters)

$s^{\prime }=distancetopointofrefraction$ (meters)

$f=focallengthoflens$ (meters)

$P=poweroflens$ (diopters)

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

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

Visual acuity equation

$(\frac{fontheight}{distancetosign})(\frac{180}{60pi})=arcminutes=a$

Note: 5Arcminutes = 20/20

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

Visual acuity (mm/metres)

$\frac{fontheight(mm)}{distancetosign(m)}\times 13.75=denominator\times of\frac{20}{x}$

Visual acuity (in/feet)

$\frac{fontheight(in)}{distancetosign(ft.)}\times 1146=denominator\times of\frac{20}{x}$

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

$typicalemmetropiceye=25mm=25,000microns$

$changeinaxiallengthof1mm=3D$

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