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115 Cards in this Set

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Sag
s = h^2 / 2r (approximation)

s = r - square root(r^2 - y^2)
Center thickness
CT = s1 - s2 + ET
Lensmaker's formula
F = n1 - n2 / r
Index of refraction
n = c / v

(speed light in a vacuum / speed light in medium)

n = lambda vacuum / lambda

(wavelength light in a vacuum / wavelength light in medium)
Snell's law and critical angle
(n1)(sin-theta1) = (n2)(sin-theta2)

Critical angle occurs when light is maximally refracted at 90-deg

Theta-c = n2 / n1
Brewster's angle
Describes how light can be polarized by refraction

tan-thetaB = n2 / n1
Malus's law
Describes intensity of light after passing through a polarizer at angle theta

I = (I)(cos^2 theta)

Theta becomes the difference between polarizer axes when light passes through multiple polarizers
Rayleigh's criteria
sin-theta = 1.22lambda / d


where d is the diameter of the aperture and theta is the angle between 2 just-resolvable objects
Minimum thickness for AR thin-film coating

Ideal index of refraction for thin-film coating
OT = lambda / 4

n = sq root(n-lens)
Equivalent power

Back vertex power

Front vertex power (neutralizing power)
Fe = F1 + F2 - (t / n)(F1)(F2)

Fv = F2 + [ F1 / (1- t/nF1) ]

Fn = F1 + [ F2 / (1- t/nF2) ]
Power and radius of curvature conversion (CL's and keratometry readings)
F = 337.5 / r
Power of spherocylinder due to curvature in an oblique meridian
F = Fs + Fc(sin^2theta)

where theta is angle of interest minus axis
Power of a mirror

Power of a prism
F = 2n / r

pD = displacement in cm / distance away in m
Prentice's rule
pD = hF

with h measured in cm
Prism deviation angle

Apical angle
d = A(n - 1)

where A is the apical angle

A is the sum of the internal angles (found using Snell's law at each prism surface)
If light enters a prism perpendicular to its first surface, at which angle does it strike the second surface?
At the apical angle
For prisms with an apical angle of less than 10deg (thin prism), angle of incidence equals what?
Apical angle


This allows for deviation calculation d = a(n-1)

Note that for a prism of n=1.5, the deviation is equal to half the apical angle
Which direction does the eye turn when a prism is placed in front (towards base or apex)?
Towards the apex
Effective power of a prism (inc/dec) when an object being viewed is moved closer to the eye.
Decreases


Since eye turns less when looking through a prism at a near object, the angle that light enters the eye is smaller.
Prism power due to thickness difference
P = 100g(n-1) / d

g = thickness diff between base and apex

d = distance btwn base and apex
Distance btwn seg OC and seg edge for

FT-28
FT-35
FT
Ribbon R-seg
Franklin (Executive) seg
Round segs
5 mm

4.5mm

0 mm (OC is at the seg line)

7 mm

0 mm

r (radius of the seg)
If seg appears too high to the patient, what adjustment should be made? Too low?
Seg too high:
1. Increase panto
2. Dec vertex distance
3. Spread nosepads
4. Move pads up
5. Stretch the bridge

Too low:
1. Narrow nosepads
2. Move pads down
3. Increase vertex distance
4. Reduce panto
5. Shrink the bridge
To calculate image jump, we find prism power of the seg where?
At the seg line (seg at the far edge)
To calculate total vertical imbalance from looking through an off-center point on a bifocal, we need prism induced by what 2 things?
1. Prism from looking away from distance OC

2. Prism from looking away from seg OC
Spectacle mag (2 formulas)
SM = Ig / Io

Ig is image size w glasses
Io is uncorrected image size

SM = (shape factor) x (power factor)

Ms = 1 / [1 - (t/n)F1 ]
Mp = 1 / (1 - hFb)

h is dist from back vertex to entrance pupil (using dist from cornea to EP as 3mm)
Relative spectacle mag
Used to compare retinal image size of corrected eye to that of standard eye (60D emmetrope)

RSM = Ia / Is

where Ia is retinal image size in corrected ametrope and Is is size in standard eye
Knapp's Law
Axial ametropes should be corrected with spectacles. RSM = 1 when a lens is placed at the primary focal point of the eye (~17mm).
Refractive ametropes are best-corrected with _______.
Contact lenses
For every 1.00 D power difference, there will be about ______% aniseikonia.
1%
Patient w a small ametropia in one eye and a >4D ametropia in the other likely is (refractive or axial?).
Axial. Should be corrected w spectacles to minimize aniseikonia.
Increasing lens thickness always (inc or dec?) SM.
Increases
Optical density
OD = log(1 / T)

where T is transmittence
Reflectance
R = [ (n2-n1) / (n2+n1) ]^2

R = 1 - T
Transmittance
After reflection: Ts = 1-R

Due to thickness: Tm = To^(t1/to)

where To is original transmittence

T = TsTsTm

(two Ts since there are 2 surfaces)
ANSI sphere power tolerance
0 to 6.50: +/-0.13D

Above 6.50: +/- 2%
ANSI cylinder power tolerance
0-2.00: +/-0.13%

2.00-4.50: +/-0.15%

>4.50: +/-4%
ANSI cyl axis tolerance
0.25D: +/-14 deg

0.50: +/-7

0.75: +/-5

1.00-1.50: +/-3

1.75 and up: +/-2
ANSI vertical and horizontal prism tolerance
Vertical: 0.33 pD

Horizontal: 0.67pD (total)
Combining prisms (4 formulas)
x = pDcos(theta) --> horizontal component
y = pDsin(theta) --> vertical component

Total pD = (x^2 + y^2)^0.5
Theta = tan^-1(y/x)
Intermediate add is usually what?
Half the near add
Most refractions are done at what vertex distance?
12mm
When is a rigid CL tear meniscus positive? Negative?
Tear lens is positive when the BC of the CL is steeper than the cornea.

Tear lens is negative when the BC of the CL is flatter than the cornea.

*This is the basis of SAM-FAP*
What is the power of the front surface of the tear meniscus for an on-K RGP if the K-reading is +45.00D? Back surface of the tear meniscus? What RGP should be chosen?
Front tear lens power = +45.00D

Back tear lens power = -45.00D

The total lacrimal lens is therefore 0D and the RGP's power should be whatever the subjective refraction shows.
Power of the tear lens in RGP wear is approx ______D for every 0.05mm difference btwn the cornea and the RGP BC.
0.25D
Javal's Rule
Estimates corneal astigmatism from K-readings

A = 1.25Ac + (-0.50 D x 90)

The second half of the equation indicates we ADD 0.50D of AR astigmatism, to account for average lenticular astigmatism
A toric RGP is indicated when residual ATR astig of _____D or WTR astig of _____D is present.
0.50D ATR

0.75D WTR
When are the following RGP's indicated?

Back toric
Front toric
Bitoric
Back toric for residual corneal astig >2.50D

Front toric for residual lenticular astig OR for corneal <2.50 and lenticular

Bitoric indicated for corneal >2.50 and lenticular
What NaFl pattern is seen in an RGP fit over WTR astigmatism? ATR astigmatism?
WTR = horizontal dumbell of touch

ATR = vertical dumbell of touch
When is RGP lens flexure helpful?
Thin RGP fit over WTR cornea will show flexure that counteracts the internal ATR astigmatism
Warpage vs flexure
Warpage occurs even when the lens is not on the eye, and is measured with a radiuscope or lensometer. Modifies BC = alters magnification properties and increases marginal astigmatism effects.

Flexure occurs with thin (usually minus) lenses due to corneal influences. When K-readings are toric over the lens, flexure has occurred.
T/F: back toric and not front toric RGP's are prism-ballasted to prevent excessive rotation.
F

Other way around - BD prism is ground into front toric RGP's
LARS
Left-add

Right-subtract

When a toric CL rotates on the eye, the rotation can be compensated for by changing the axis
Dk vs T
Dk = lens oxygen permeability (P), where D is gas diffusivity and k is gas solubility

T is lens oxygen transmissivity, which takes into account lens thickness

T = P/t = Dk/t
High water content corresponds to (high or low?) Dk for HEMA lenses. For SiHy lenses?
High for HEMA, low for SiHy
Magnification by a thin lens is achieved by placing the object where relative to the primary focal point?
Inside F
Relative distance mag
RDM = d1/d2
Mag by a thin lens is a combo of what?
Lateral mag of the lens and RDM of the object
FDA SCL groups
Group 1 - low H2O, non-ionic

Group 2 - high H2O, ionic

Group 3 - low H2O, non-ionic

Group 4 - high H2O, ionic
A collimating magnifier results when the object is placed where?
At the focal point of the magnifying lens
Low vision Tx is appropriate when VA is worse than what level?
20/60
M-notation significance

Conversion from Snellen to M

1M at distance is what-sized letter? At near?
M-notation is a linear scale that is based on the 20/20 Snellen letter from 1M away. Convenient bc it can be directly correlated to necessary magnification for 20/20 vision - if a patient can read the 20/800 letter at 40cm, this correlates to 14M, and we know the patient needs 14X mag to see 1M (20/20).

Measure Snellen letter and divide by 1.45 to convert to M-notation

20/20 letter from 1Mm away is "1M" (1.45mm)

Bringing the card to 40cm (2.5x closer) gives 1M = 20/20 x 2.5 = 20/50 letter.
20/20 Snellen letter subtends how many min/arc from 20 feet or 6m?

What is the size of this letter in mm?
5 min/arc

8.77mm
Advantages of ETDRS chart?
1. Log progression of 0.1log units between each line

2. Uniform contrast

3. Separation btwn letters = letter size

4. Metric recordings can easily be converted to Snellen when measured at 1, 2, or 4m.

1m = x 20
2m = x 10
4m = x 5
What is a normal CS as measured by Mars or Pelli-Robson?
1.52 - 1.76 logCS for people over age 60

1.72 - 1.92 logCS for people <60

Severe CS loss is anything <1.00 logCS
T/F: Poor CS benefits from increased mag
F

A patient w/ moderate CS loss (<1.4 logCS) will not benefit from increased mag.

They will benefit from increased illumination.
Impairment vs disability vs handicap
Impairment is any anatomical or physiological deficit/abnormality (e.g. legal blindness).

Disability is a lack of ability within normal range resulting from an impairment (e.g. not being able to read small print).

Handicap is a disadvantage resulting from an impairment or disability that limits or prevents fulfillment of a normal role for that person (e.g. paying your bills).
BAT for differentiating btwn amblyopia and ocular disease etiology for vision loss
VA is not reduced in amblyopia

VA is reduced by ~2 lines in ocular pathology
What is the disadvantage for using a reverse Galilean telescope to enhance FOV?
Proportionate minification

e.g. gain 3X FOV but view is minified to 1/3 original size
What strategy is most commonly used by patients w/ restricted FOV's?

When using a Fresnel prism to increase FOV, in which direction does the base point?
Scanning

Base towards the blind side
Amsler grid held at 33cm (11in) tests ____degrees and requires a ____ add.
10 degrees (central)

+3.00
What is the Snellen acuity of large-print books?
20/100 or 2M
Effective magnification
Magnification based on a standard reading distance of 25cm ("least distance of distinct vision" or "reference seeing distance").

This means the standard emmetropic, presbyopic patient needs a +4.00D add to read clearly.

Gives convention that a +4.00D lens has a magnification of 1X.

Magnification = F(0.25m) = F / 4

Can use this only when:
1. object is 25cm from spectacle plane
2. object is held at F of the magnifier

*Manipulate this eqn for different reading distances - AM = F(distance)
Conventional magnification
Similar to effective mag, but considers that the original object of regard requires +4.00D of accommodation at 25cm, before any lenses are introduced at all.

Mag = F/4 = 4/4 = 1X --> one additional unit of mag should be added to effective mag

Conventional mag = F/4 + 1
Definition of angular mag
Enlargement of the image is completely created by the optics of the device being used

AM = 1 + hF

where h = distance of magnifier from spectacle plane

All LV devices have angular mag, but we think of HAND MAGNIFIERS and TELESCOPES mostly
Equivalent power of LV devices
Feq = F1 + F2 - c(F1)(F2)

F1 = power LV device
F2 = power add or accommodation
c = separation of LV device from spectacle plane
When the object being viewed w/ a LV device is held at the focal point of the device, what is Feq? Is accommodation or an add necessary? Does lens power depend on distance the eye is from the LV device?
Feq = power LV device when object is held at the focal point

No accommodation or add is necessary when and object is held at the focal point

Lens power does not vary with distance the observer's eye is from the lens when the object being viewed is at the focal point of the lens
Kestenbaum vs Lighthouse vs Acuity Reserve methods for determining initial add power in LV
Kestenbaum - based on reciprocal of Snellen BCDVA

E.g. BCDVA 20/100 --> take reciprocal 100/20 = +5.00D add necessary for 1M print

Lighthouse - place +2.50 add above the distance Rx; use RDM to determine initial predicted add

E.g. Patient reads 2M at 40cm using +2.50 add -->needs to bring card to 20cm to achieve 2X to read 1M - this requires +5.00D total add

Acuity reserve - 2X predicted add to achieve acuity reserve for fluent reading
High-plus spectacles induce prism at near. What compensating prism strenghts are usually incorporated into the following high-plus Rx's?

+4.00D
+6.00D
+10.00D
+4.00 = 6BI each eye

+6.00 = 8BI each eye

+10.00 = 12 BI each eye
Binocular convergence demand for close reading distances
BCD = pupillary distance (cm) / reading distance (m)
When should an add be used with a hand magnifier? When should distance Rx be used?
Based on Feq = F1 + F2 - cF1F2

Use add when distance HM is from the spectacle plane is closer than f1

Use either when distance is equal to f1

Use distance Rx when distance is farther than f1
Linear FOV through hand magnifier
w = d / Fh

where d = lens diameter, h = distance of lens from the eye

*If magnifier is held one focal length away from the eye, FOV = diameter of the magnifier

*If magnifier is held 2 focal lengths away from the eye, FOV is 1/2 the diameter
The object distance for a stand magnifier is (less than/more than) the focal length of the lens.
Less than

This is why an ADD is necessary for a stand magnifier
What type of image does a stand magnifier create?

e.g. virtual/real, upright/inverted, convergent/divergent
Virtual, upright, divergent
Equivalent power of a stand magnifier
Feq = (enlargement ratio)(add)

ER = (U' - Fm) / U'

where u' is the image vergence
Fm is the equivalent power of the plus lens

ER can usually be read off the device
Galilean telescope:

Tube length (L)
Ocular is (+/-), objective is (+/-)
Location of exit pupil
Final image is (inverted/erect)
(Small/large) FOV
Available in F up to ___X
L = 1/Fobj - 1/Foc
Ocular is (-), objective is (+)
Exit pupil is inside the telescope
Final image is erect
Small FOV
Keplerian telescope:

Tube length (L)
Ocular is (+/-), objective is (+/-)
Location of exit pupil
Final image is (inverted/erect)
(Small/large) FOV
L = Fobj + Foc
Ocular is (+), objective is (+)
Exit pupil floats outside telescope
Final image is inverted
Large FOV
The (entrance/exit) pupil of a telescope is usually the objective lens.
Entrance pupil
Magnification by a telescope
M = - (Foc/Fobj)
Exit pupil of a telescope is the image of the (obj/oc) lens through the (obj/oc)
Exit pupil is the image of the objective lens through the ocular lens
How are telescopes labeled?
Magnification x objective lens diameter
What is the size of the exit pupil for a 5 x 45 telescope?
5 is the magnification
45 mm is the diameter of the objective

The image of the objective by the ocular is the exit pupil

Exit pupil = 45mm / 5X = 9mm
Definition of legal blindness
Best-corrected acuity of 20/200 or worse in the better-seeing eye OR visual field diameter of 20-deg or less in the better eye
Far point/ near point determination
Use B = L + O + A + D

with B (blur) = 0
The far point for an emmetrope is ___.

The far point for a myope is (real/virtual) and for a hyperope is (real/virtual).
Emmetropic far point is inifinity.

Myopic FP is real, hyperopic FP is virtual.
"Rule of 30"
Axis of correcting Rx can be found by asking patient which clock dial is most clear, and multiplying by 30.

E.g. 3:00 - 9:00 line is clearest --> 3 x 30 = 90 degrees
Which is the only Purkinje image that is not virtual and upright?

Which is the largest Purkinje image?
Image IV (posterior lens) is real and inverted, since this is the only surface that is concave

I is anterior cornea
II is posterior cornea
III is anterior lens

Purkinje images get generally smaller from I - IV, except image III is the largest

Purkinje images get progressively more dim
How does Purkinje image size change with accommodation?
No accommodation: III > I > II > IV

Accommodation: I > II > III > IV since image III moves back and image IV moves forward
What does increasing panto do to the power of a lens?

Increasing faceform?
Increased panto = induction of cylinder w/ axis of 90 (minus cyl form)

Increased faceform induces cyl at an axis of 180 (minus cyl form)

*Axis of the induced cylinder is the same as the axis of rotation!*
T/F: the cornea acts like a high-+ lens in keratometry
F

The cornea acts like a MIRROR, and specifically acts like a negative (convex) mirror
T/F: the cornea acts like a high-+ lens in keratometry
F

The cornea acts like a MIRROR, and specifically acts like a negative (convex) mirror
T/F: Image jump is independent of distance Rx.
T

Only dependent on the power of the add.
A Keplerian telescope w/ a higher-powered ocular lens has (more/less) magnification and a (smaller/larger) exit pupil
Higher-powered ocular gives MORE magnification.

More magnification gives a SMALLER exit pupil.

Mag = diameter ent / diameter exit
MAR = ?
1 / Snellen acuity
What is the M-acuity for a patient who reads 1.5M at 60cm?
0.60 / 1.5 = 0.4M
Nott retinoscopy vs MEM
MEM uses lenses to neutralize the reflex

Nott uses change in distance to neutralize the reflex
How does aperture size affect spherical aberration?
Sph aberration is proportional to the square of the entrance pupil diameter.

E.g. doubling aperture will double the entrance pupil and quadruple the spherical aberration
Schematic eye: generally, where are the principal planes? Nodal points? Anterior and secondary focal points?
PP's - in the anterior chamber (1.35 and 1.60mm behind anterior cornea)

NP's: back surface of the lens (7.09 and 7.33mm from anterior cornea)

F is ~16mm in front of the anterior cornea

F' is ~25mm behind the anterior cornea (behind the retina)
The simplified Gullstrand model eye has three refracting surfaces and is used to calculate postitions of the ______ and ______ (to determine visual axes and angles)

The Reduced Eye has a single convex refracting surface and is used to calculate __________ in ametropic eyes.
Gullstrand: calculate entrance & exit pupils

Reduced: calculate retinal image size in ametropic eyes
T/F: in the schematic eye (Gullstrand no 1), the secondary focal point is at the retina.
F - it's just behind the retina


F' is on the retina in the simlified schematic eye (Gullstrand #2) and the reduced eye
Angles of the eye:

Alpha
Lambda
Kappa
Gamma
Angle alpha - btwn optical and visual axes, formed at the nodal point

Lambda - btwn pupillary axis and line of sight, formed at the center of the entrance pupil

Kappa - btwn pupillary and visual axes (NOT A TRUE ANGLE)

Gamma - btwn fixation axis and optical axis
Axes of the eye:

Optical axis
Visual axis
Pupillary axis
LOS
Fixation axis
Visual axis - line connecting centers of curvature of various optical elements of the eye; goes through the nodal points and is perpendicular to all refracting surfaces

Visual - connects fixation point, nodal points, and fovea

Pupillary - normal to the cornea, passes through center of entrance pupil

LOS - connects fixation point and center of the entrance pupil

Fixation axis - fixation point to the center of rotation of the globe
Purkinje image 1 (corneal reflex) indicates the approximate position where which axis intersects the cornea?

What indicates the pupillary axis position?


Angle ___ is formed at the entrance pupil

Angle ____ is formed at the nodal point.
Line of sight

Center of the entrance pupil

Lambda (intersection of pupillary axis and LOS)

Alpha (intersection of pupillary axis and LOS)
Dimensions of the optic disc in degrees?

How far is the center of the fovea form the ON (degrees)?

How large is the macula?

How far is the center of the fovea from the posterior pole?
ON is 5deg wide x 7deg high

Center of fovea is 15deg from the ON

Macula is 5deg

Center of the fovea is 5deg from the posterior pole
1 degree = ____ arcminutes

T/F: when using Rayleigh's criterion to find MAR, we must convert degrees to MAR in order to get to Snellen VA
60

T!
If we avoid trig functions, we can make the small-angle approximation. This gives angles in (degrees or radians?).

Conversion between rad and deg?
Small angle approx gives angle in RADIANS

1 deg = rad(180/pi)