NBEO Part 1 Equations

how to calculate AC/A?

PD (in cm)+ fixation distance (m) (near phoria - dist phoria)

eso is +

exo is -

how to calculate power of a mirror?

D = -(2n/r)

c-shaped = pos radius

backwards c = neg radius

a convex mirror is (converging/diverging)

diverging

+r

*opposite of lenses

a concave mirror is (converging/diverging)

converging

-r

*opposite of lens

according to Kestenbaum's rule how can we calculate an add?

inverse of dist acuity tells us add needed to read 1M (20/50 at 40cm)

*note you need to change this add if the target is ANYTHING other than 1M

how to calculate FOV?

W = d(f/h)

W - FOV

d - dam of lens

f - focal length

h - vertex distance

formula for effective magnification?

M = D/4

M - mag

D - power of lens

formula for conventional magnification?

M = (D/4) + 1

M - mag

D - power of lens

how to calculate mag of a telescope

M = - (Doc/Dobj)

how to calculate tube length of a telescope?

TL = (1/Doc) + (1/Dobj)

given a reading cap power and a telescope mag what is the equivalent power?

Mtel*(reading cap) = Deq

what is the effectivity eq?

Dnew = (Dold) / 1-(h)(Dold)

when to use effectivity eq?

vertexing, effectivity, spec/CL

what is the equation for back vertex power?

Dback = ((D1) / 1-(t/n)(D1) +D2)

*can be reversed to calculate front vertex power

how to calculate equivalent power of a thick lens?

De = D1 + D2 + (t/n)D1D2

what is the RGP equation?

Cornea = Dtear lens + Dcl + Dover refraction

what is the CL power equation?

D = 337/r

*r is in mm!!

what is Javal's rule?

Arx = 1.25(Ac) + (-0.50x090)

or

Arx = 1.25(Ac) + (+0.50x180)

how do I calculate prism deviation?

pd = (displacement (cm))/distance (m)

what is prentice's rule?

pd = dD

d - distance from OC (cm)

D - lens power (in appropriate meridian)

how to calculate deviation angle?

deviation = A(n-1)

pd = deg1.75

what is the lensometer equation?

x=f^2(Fv)

x = distance lens target is moved

f = focal length of std lens

Fv = back vertex power

*target moved closer to viewer = plus lens

*target moved farther from viewer = minus lens

how to calculate power in DO?

DO = patient Rx + Dr Rx

how to calibrate lens clock?

True DL = ((n lens material - 1)/ (n calibration -1))*DLC

*lens clock reading only accurate if clock is calibrated for the n of lens material

how to calculate decentration?

d = (frame PD - patient PD) / 2

how to calculate lens thickness?

CT - ET =S1 - S2

D = (2s(n2 -n1))/(h^2)

D - power of lens surface

s - sag

h - half diameter of lens

how to calculate minimum blank size?

M = ED + 2(d) + 2mm *done in mm

ED = effective diameter

d = decentration

how to calculate frame pd (GCD)?

frame pd = A + DBL

how to calculate seg inset?

seg inset = (dist pd - near pd) /2

*MRP --> near OC

how to calculate inset?

inset = (frame pd - dist pd) /2

how to calculate total inset?

total inset = (frame pd - near pd) / 2

how to calculate chromatic aberration?

CA = D/ABBE

*this is why we want a HIGH ABBE

if an image or object is found in object space it is (negative/positive)

negative

*in front of the lens

if an image or object is found in image space it is (negative/positive)

positive

*behind the lens

what is the equation for object location?

u = (n1/U)

*n is for whatever material you are in

U + D = V

what is the equation for image location?

v = (n2/V)

*n is for whatever material you are in

U + D = V

how to calculate power of an SSRI (lens maker equation)?

D = (n2 - n1) / r

*nto minus nfrom

how to calculate lateral mag?

m = (hi/ho) = U/V

*+m = upright

*-m = inverted

as light travels, vergence gets (more/less) plus

MORE PLUS

*CL Rx is ALWAYS more plus than specs

(concave/convex) interface wraps around the lower n medium

concave

*always a diverging surface

*caves into lower index

(concave/convex) interface wraps around the higher n medium

convex

*always a converging surface

*covers higher index

an object at the primary focal point (F1), will have ___ light leaving

parallel (V = 0)

*primary focal length is the distance from the interface to F1

*secondary starts straight

an image at the secondary focal point (F2), is formed by __ light entering

parallel (U = 0)

*secondary focal length is the distance from the interface to F2

*primary departs parallel

when are primary focal points clinically relevant?

telescopes

lensometer

HHM**

clinically we use Snell's law during....

gonioscopy (can view the angle because of total internal reflection)

according to Snell's law what 2 factors impact how light is bent/refracted?

1. angle light hits a surface

2. index of refraction

according to Snell's law...

lower n = light travel's (faster/slower)

higher n = light travel's (faster/slower)

faster

slower (slower in dense mediums)

when is total internal reflection possible?

when n2 > n1

when do we apply depth of focus clinically?

pinhole (inc FOV, inc inverval of clarity)

night myopia (dec DOF with larger pupil)

lag/lead of accom

___ is the dioptric point of best focus for a lens

circle of least confusion

__ is the linear distance between the locations of horizontal and vertical line formations

interval of Stern

___ is the physical entity that limits the amount of light entering an optical system

aperture stop

*limits FOV

___ limits the size of the object that can be imaged by the system (limits # of off axis rays entering)

field stop

___ is the image of the aperture stop formed by all the lenses in front of it

entrance pupil

*note if no lenses in front, entrance pupil itself is the aperture stop

___ is the image of the aperture stop formed by all the lenses behind it

exit pupil

*note: if no lenses behind it, exit pupil itself is the aperture stop

LASIK requirements;

__ microns must remain under the the flap to maintain corneal integrity

the flap is approx __ microns thick

ablation depth is approx __ microns/diopter

250 micons

150 microns

12 microns/D

what is the distance between OC and edge of the bifocal segment for a flat top 28 (or less) seg?

5 mm

what is the distance between OC and edge of the bifocal segment for a FT 35 seg?

4.5 mm

what is the distance between OC and edge of the bifocal segment for an executive or Franklin seg?

0mm

what is the distance between OC and edge of the bifocal segment for a round segment?

radius of the seg

ex round 22 = 11mm

how to calculate image jump?

pd = dD

d = seg height (cm)

D = power of the add (DONT need distance RX)

how to inc spec mag of a PLUS lens?

inc vertex distance*

inc thickness

inc BC

dec n

how to inc spec mag of a MINUS lens?

dec vertex distance*

inc thickness

inc BC

decrease n

when to use a spherical GP?

cyl <0.75

when to use a front toric GP?

corneal cyl <2.50 and >0.75D residual astig

when to use a back toric GP?

>2.50D corneal cyl and spec cyl = 1.5*kcyl

when to use bitoric GP?

>2.50D corneal cyl and spec cyl ≠ 1.5*kcyl

what's Sheard's criterion?

(2/3)phoria - (1/3)(compensating vergence)

what's percival's criterion?

P= (2/3)G - (1/3)L

G = greater of vergence ranges

L = lesser of vergence ranges

P = 0 or neg # no prism is needed

given a Keplarian telescope and Galilean telescope of equal magnification, diameter, and objective lens power, which will provide largest FOV?

Keplarian

*exit pupil closer to the eye than with a Galilean telescope

for every 5º of CL rotation, induced cylinder is ___ of the original power

1/6th

*ex if lens rotates 15º, then cyl power is half the original power

what is the Munnerlyn equation to determine ablation zone diameter for LASIK?

AD = (AZD^2*D)/3

AD = ablation depth

AZD = ablation zone diameter

D = diopters of correction

BD prism is ground into PALs to minimize thickness differences, how do you calculate how much prism should be ground in?

pd = (2/3)add

what wavelengths of light are most likely to damage the retina of a phakic elderly adult?

UV-A (400-315)

*with yellowing of crystalline lens it absorbs UV-B light (315-280nm) and almost all UV-A light

what types of UV light are absorbed by tears, cornea, and aqueous humor?

UV-C

at what age does VA of a child reach adult levels?

3-4 years