KMK Optics Boards formulas/numbers

vergence

L' = F + L

L'=image vergence

F=power of the objective lens

L=object vergence

Obj and img location

l = n₁/L

l' = n₂/L'

CL thickness

(ct) = 0.023 x contact lens power (CLP) + 0.19mm

similar triangles for retinal image size

o/a=i/b

uses nodal point=point on the axis through which light passes undeviated

lateral mag

M = hi/ho = L/L'=l'/l

L=object

L'=image vergence

l'=image locaiton

l=object location

downstream (effective) vergence (like if using a stand magnifier)

Leff = L/1-dL

L= vergence leaving lens power

d = how far away magnifier is from spec plane or eye (in mm)

power and vertex distance

Fc = Fg/1 - d Fg

Fc = desired power at cornea

Fg = power of lens needed at the vertex distance

d = vertex distance

power of mirrors

F = -2n/r

- because continuing to use the C+ rule

power of SSRI

F = n₂-n₁/r

r = radius - will be + or - based on vex/cave of surface that the light is leaving

C+ gets you through optics (c shaped radius=+)

thin lenses

Ft = F₁+F₂

apparent depth

n₁/l = n₂/l'

thick lenses - equivalent power

Fe = F₁+F₂ - t/n₂F₁F₂

back vertex power

Fv = F₂+ F₁/(1-t/n₂F₁)

lensometer

x = f²Fv₁

Fv₁= back vertex power

radius of curvature

F = n₂-n₁/r

lens clock

Fl = nL-1/nLc-1 (FLc)

Fl = power from lens sag in diopters

nL = index of ref of lens

nLc = index of ref needed to calibrate lens clock (or index of lens clock)

FLc = power of readout of lensclock

lens thickness

s = h²/2r

h = half chord length (1/2 diam lens)

tC-tE = S₁-S₂

tE,tC <->S₁,S₂<->r₁,r₂<->F₁,F₂

(just draw a pic of vex/cave lenses to find thickness and sag)

then can calculate lens power thickness with: F = n₂-n₁/r

decentration per lens

d = frame PD - wearer's PD/2

minimum lens blank size

M = ED+2(d)+2mm

**in mm!!**

ED = effective diam

d = decentration from FPD-WPD/2

petzval surface

K=F/n

K = curvature of image surface (for dist obj)

abbe number / chromatic aberration

CA = F/v

CA = chromatic aberration

v = abbe value

achromatic doublet

-F₁/V₁ = F₂/V₂

-combine + lens of one material with a - lens of another material to eliminate chromatic aberration

deviation power

Δ = y/x

prism power & apex angle

d = A(n-1)

d = deviation angle

A = apex angle in deg

"dan-1"

prism power and thickness

Δ = 100 g(h-1)/l

g = diff in thickness b/w apex & base

l = apex to base length (same units as g)

prentice's rule - prism decentration

Δ = dF

(P = dF)

d needs to be in cm!!!j

Pythagorean's if horizontal/vertical aspect

Δ^2=H^2+V^2

spectacle mag

SM = Ig/Io

Ig = w/ glasses

Io = w/o glasses

SM = shape factor x power factor

shape factor

Ms = 1/1-(t/n)F₁'

t = central thickness

F₁' = front surface power

power factor

Mp = 1/1-hFv'

h = dist b/w back surface of lens & entrance pupil of eye (vertex+3 mm)

Fv' = back vertex power of lens

vertex distance

(for CL power required for given SRx)

Fc = Fs/1-dFs

Fc = refractive power measured at cornea

Fs = '' measured at vertex distance (spectacle distance)

d = vertex distance

lacrimal lens

Rc = FcL+Fll+FoR

Rc = refraction at cornea

Javal's rule

ARx = 1.25(Ac) + (-0.50 x 90)

ARx = total refractive astigmatism

Ac = corneal astigmatism

2nd term just says "add 0.50 ATR cyl,"

which is the the average residual (non-corneal) cyl

half amp method - to find add

a = Wd - Aa/2

a = add

Wd = working dist

Aa = accom amp

calculated AC/A

AC/A = PD + NFD (Pn-Pd)

phoria at near - phoria at distance

PD in cm!!!!

NFD = meters for near fixation distance

eso is+, exo is -

gradient AC/A

AC/A = (P₁-P₂)/(SA₁-SA₂)

P's = phorias under 1st & 2nd condition

SA's = accom stim under 1st & 2nd condition

sheard's - figure out how much prism to Rx to eso/exo pt

S = 2/3D-1/3R

D = phoria demand

R = compensating fusional vergence reserve

compensatory fusional vergence reserve (blur point) should be at least twice the demand of the phoria

most effective for exo prism Rx?

use blur points

percival's

P = 1/3G - 2/3L

-lesser fusional vergence reserve should be at least half the greater reserve (doesn't take into account phoria of pt)

most effective for eso prism Rx?

use blur points

accom amps

avg: 18.5 - 0.3(age)

min: 15 - 0.25(age)

max: 25 - 0.4(age)

power tolerance - ansi stand

sph:

-6.50 - +6.50 = +/-0.13

> +/-6.50 = +/-2% sph power

cyl:

<2.00 = +/-0.13

2.00-4.50 = +/-0.15

>4.50 = 4% cyl power

axis tolerances - ansi stand

0.25 or less = +/-14

>0.25 to <0.50 = +/-7

>0.50 to <0.75 = +/-5

>0.75 to <1.50 = +/-3

>1.50= +/-2

vertical prism tolerances - ansi stand

0 to < +/- 3.375 = < 0.33

> +/- 3.375 = < 1mm difference in height of PRPs

horizontal prism tolerances - ansi stand

0 to < +/- 2.75 = < 0.67

> +/- 2.75 = < +/- 2.5mm from specific difference interpupillary distance

ansi Z80.1-2015 tolerances

thickness = +/- 0.3mm

warpage = 1.00D

base curve = +/- 0.75D

impact = resists 5/8in steel ball from 50in

high mass impact (drop ball test)

Pointed projectile, 500 g, dropped from 50 inches

High velocity impact

steel ball, 0.25in in diameter, fired at 150ft per sec

ophthalmic crown glass

n = 1.523

Abbe = 58.9

CR-39 (plastic)

n = 1.498

Abbe = 58

polycarbonate (plastic)

n = 1.586

Abbe = 30

Trivex

n = 1.53

Abbe = 44

reflectance and transmittance and absorption

((n2-n1)/(n2+n1))^2=R

R=reflected. Has to be done at both surfaces but same at both surfaces if in air

Transmittance:

Ts=1-R

Absorbed by medium:

Tm=1-(amount of light absorbed by lens)

Total transmittance:

T=(Ts1)(Ts2)(Tm)

Should be like (0.96)(0.96)(0.70)=0.65

Ideal thin film (AR) coating

nf=sq(n1nL)

nf is index of film

n1 is index of initial medium

nL is index of lens material

sqr of n basically

mm to D (CL)

F=337.5/r

r=337.5/F

add 0.8 to 1 mm to this to get CL BC

in mm

total mag by HHM

M=uF

absolute value of u=original distance between object and eye. F is power of magnifier

standard distance of 0.25 M

so F/4 is store labelled magnification

used at primary focal point. 10 D lens primary focal point is 1/10= 10 cm

U of Florida equation

linear field of view with HHM

w=d/(Fel)

d= dimater of the lens

Fe=equivalent power

d=distance between magnifier and spectacle plane

stand magnifier

total angular magnification:

Mt=mM

m=lateral magnification

M=relative distance magnification

Total magnification of stand magnifier+add lens system

M=Fe/4

Fe=equivalent power of the stand magnifier-add system

Max mag:

Mmax=(F/4)+1

tube length of telescope

d=fobj+foc

focal length of objective+focal length of the ocular

angular magnification of telescope

M=-(Foc/Fobj)

don't forget the minus!

M=dEnt/dEx

d of entrance pupil/ diameter of the exit pupil.

entrance pupil is the objective lens, exit pupil is the image of the objective lens seen through the ocular.

dent over dex

telescope labelled A x B

A is magnification

B is objective lens diameter

5 x 45

5x mag, B is 45 mm objective lens diameter. Also diameter of entrance pupil as a result

magnification of a telemicroscope

Total Mag=Mag of reading cap x Mag of telescope

Mag of cap=original distance x F

Mag of cap=F/4 (Standard equation)

primary focal point for reading cap is working distance

classifying vision

normal: 20/12-20/25

near normal: 20/30-20/60

Moderate: 20/70-20/160 (BI prism)(>=+4 Add? Give 2+Dioptric power of lens BI prism per eye)

Severe low vision: 20/200-20/400 (Monocular)

Legally blind (at least one of two): 1. patient cannot read any letters on 20/100 in better seeing eye (but classically it's 20/200 or worse in better seeing eye)

2. visual field diameter is 20 degrees or less in better seeing eye

M letter

5 arcminutes at 1 M (20/20 snellen) (1.45 mm tall)

test distance in m/M unit= 20 feet/size of the snellen letter

JND

denominator of the 20 ft snellen acuity /100

magnification required

distance magnification = current distance BCVA/goal distance BCVA

near magnification=current near BCVA/goal near BCVA x working distance

using M notation, this is the lighthouse method

kestenbaum's rule

inverse of patient's distance visual acuity to determine the starting add power

BCVA 20/200

predicted add is 200/20=+10D

newspaper print

1M at 40 cm

reduced eye

n=1.33

22.22 axial length

60 D

4 equations that don't use meters only

minimum blank size

prism

Contact lens power equation

calculated AC/A

cpd to snell

600/cpd=snellen denominator

flip snellen for MAR. 20/50-->50/20=2.5

4 cpd=low

40-60 cpd=high

cataracts affects all cpd equally

snell's law

n1sinθ1 = n2sinθ2

n2/n1=sinθc=critical angle

interval of sturm

linear range of clear vision between sph and sph+cyl

Circe of least confusion

dioptric location of clearest vision in spherocylindrical lens

lens/mirror combination

F=2F1+F2

f1 is power of front surface of lens and F2 is power of mirror

F=(n2-n1)/r

reduced thickneses

F=t/n

amt of candellas falling on a surface

(initial candellas)/d^2

Distance from surface=d

estimate pinhole acuity

2.33/d

d in mm

Snellen to point

(snellen denominator)/6=point notation

Munnerlyn equation

d^2/3=l

ablation depth per diopter for traditional lasic.

d= ablation diameter in mm

l=ablation depth in microns

rough estimate is 12 microns per diopter for traditional LASIK

15 for wavegront guided lasik? (40% more than traditional)

spectrums

UV

Visible

Infrared

UV: 1-400

Visible: 380-760

Infrared: 700-10^5

UVC-100-280

UVB-280-315

UVA-315-400

power of the prism

P=(100)(x/d)

Where P= power of the prism (in prism diopters, pd), x= the total distance that a ray of light is deviated, and d= the total distance from the prism to the location where the deviation is measured.

Bailey-Lovie chart to snellen

When recording visual acuity using a Bailey-Lovie visual acuity chart, the numerator will be your testing distance, which in this case is 8 feet. The denominator will require you to think about the logarithmic progression of the size of letters on this type of chart. We know that 1.0 LogMAR is a letter size of 200, and each line below decreases by 0.1 logMAR (or 1.26x smaller). So, working your way down the chart, 0.9 LogMAR is a 160 size letter, 0.8 LogMAR is a 125 size letter, 0.7 LogMAR is a 100 size letter, 0.6 LogMAR is an 80 size letter, and 0.5 LogMAR is a 63 size letter.

lens in air to lens in water

D(air)/D(water) = n(lens) - n(air)/n(lens) - n(water)

front and back of thick lens

A thick lens has two refracting surfaces. The refractive power of the second surface is determined by using the equation P= (n-n')/r. The power of the first refractive surface is calculated via use of the equation P= (n'-n)/r.

thickness of AR coating

thickness=wavelength/4n

height of snellen letter

8.73 mm