Visual and Applied Optics 1 > MATHS > Flashcards

MATHS Flashcards

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1
Q

Sign Conventions for Optical Calculations

A

Measurements to the RIGHT of a surface/lens are POSITIVE

Measurements to the LEFT of a surface/lens are NEGATIVE

Measurements BELOW a surface/lens are NEGATIVE

Measurements ABOVE a surface/lens are POSITIVE

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2
Q

Snell’s Law

A

n sin(i) = n’ sin(i’)

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3
Q

What sign are clockwise angles?

What sign are anticlockwise angles?

A

NEGATIVE

POSITIVE

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4
Q

If you increase the centre thickness of a lens, does that make it more positive or more negative?

A

More positive

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5
Q

Refractive Index of a medium formula

A

velocity of light in a vacuum/velocity of light in a medium

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6
Q

Power of a Spherical Refracting Surface formula (F)

A

F = (n’ - n)/r

OR

F = (refractive index of new medium - refractive index of previous medium)/r

r - metres

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7
Q

What would you do for THIN lenses once you have worked out the front and rear surface powers and why would you do this?

A

For THIN lenses, you can just add the 2 powers (front and rear surface) together to get the overall power of the THIN lens.

This is because it doesn’t take into account the centre of thickness

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8
Q

The exact sag formula

A

s = r - √ (r^2 – y^2)

r - radius of curvature
y - half of the chord diameter

Error increases as the power increases

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9
Q

What surface does the exact sag formula apply to?

A

SPHERICAL SURFACES ONLY

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10
Q

What do we mean by the term “sag”?

A

Describes how much material needs to be removed

Distance between vertex of curve to end of curve

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11
Q

Lens measure – a simple device for measuring surface power

A

outer two are fixed (determines chord); middle one moves to control needle position

So, the spacing of the outer pins on the lens measure will give 2y
The length of the centre pin will give s

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12
Q

Rearranged sag formula to calculate r

A

r = (y^2 + s^2)/2s

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13
Q

What refractive index do lens measures normally assume?

A

1.523 (Ophthalmic Crown Glass)

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14
Q

Formula if the lens is made from another material than Ophthalmic Crown Glass (1.523)

A

Ftrue = Fmeasured x ((ntrue – 1) / 0.523)

Ftrue - True surface power

ntrue - Actual refractive index of lens

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15
Q

BVP (short formula)

A

BVP = 1/Back vertex focal length

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16
Q

BVP

A

BVP = [ F1 / 1-(t/n’ x F1) ] + F2

F1 = the surface power of the front surface of the lens (D)

F2 = the surface power of the back surface of the lens (D)

t = the centre thickness of the lens (metres)

n‘ = the refractive index of the lens material

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17
Q

FVP

A

FVP = [ F2 / 1-(t/n’ x F2) ] + F1

F1 = the surface power of the front surface of the lens (D)

F2 = the surface power of the back surface of the lens (D)

t = the centre thickness of the lens (metres)

n‘ = the refractive index of the lens material

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18
Q

What effect does a Plano surface have on positive power with respect to centre of thickness?

A

-ve lens : centre of thickness doesn’t impact +ve power

+ve lens : increasing centre of thickness = increasing +ve power

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19
Q

Approximate Sag Formula

A

s = y^2/2r

STICK TO OTHER SAG FORMULA

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20
Q

What are the different Lens Forms for Flat Form Convex Lenses?

A

Plano convex - one convex surface, one plano surface

Bi-convex - 2 convex surfaces of differing radius

Equi-convex - 2 convex surfaces of equal radius

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21
Q

What are the different Lens Forms for Flat Form Concave Lenses?

A

Plano concave - one concave surface, one plano surface

Bi-convex - 2 concave surfaces of differing radius

Equi-convex - 2 concave surfaces of equal radius

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22
Q

What are the different Lens Forms for Meniscus or Curved Form Lenses?

A

Front surface = convex
Back surface = concave
-ve power outweighs +ve power, so lens has a -ve power

OR

+ve power outweighs -ve power, so lens has a +ve power

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23
Q

Lens Form Equation

A

Tc + S2 = Te + S1

Tc - Centre thickness
S2 - Sag of back surface
Te - Edge thickness
S1 - Sag of front surface

NOTE : FOR A PLANO CONCAVE LENS S1=0

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24
Q

What happens when you increase the base curve (front surface power of a lens)?

A

The front and back Sag increases
Edge thickness increases

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25
temporal y + nasal y =
horizontal lens size Reducing temporal y = reducing lens thickness
26
Considerations for lens thickness for a myope
-Large box size = increases edge thickness (keep field of view in mind) -Avoid frames with points away from the optical centre -Try to match geometric centres of glasses with Px's PD -Choose a frame with the BVD as small as possible
27
Considerations for lens thickness for a hyperope
-Choose a high refractive index material -Consider an aspheric lens design
28
Why do we prescribe Prism?
-Used to help a Px cope with heterophoria (where eyes misalign when they are not focussing together) -Helps Px's if they have had a stroke (muscles in the eye don't allow for proper and full movement) -Corrects fixation disparity (misalignment in the visual axis of the eyes) -Helps reduce double vision in some types of heterotropia (where the eyes cannot focus on the same object simultaneously) -Helps with convergence insufficiency
29
Where does a Prism deviate light to?
Deviates light towards the base The image moves towards the apex
30
What are the 2 forms of prism?
Flat form - trial case lenses Curved form - incorporated into spectacle lenses
31
Formula to calculate Deviation Angle, d
d = (n'-1)a GOOD FOR CALCULATIONS WHEN THE APICAL ANGLE, a IS 10 DEGREES OR LESS
32
Formula to calculate Prism Power, P
P = 100tan(d) NOTE : If you have an object 1m (100cm) away and you have 1∆ prism ; then it will deviate the light by 1cm
33
What unit is Prism Power measured in and what symbol does it have?
Prism dioptres Symbol - ∆
34
Thickness difference of prisms formula
P = [100(n'-1)g ] / D P - Prism power g - Prism thickness difference g = Thick edge - Thin edge D - Diameter
35
How do you interpret Prismatic power by focimetry? (corona type target)
From the middle of the target (middle of the circular target), draw a up/down and left/right and read off using the scale NOTE : We can also use a Prism Compensator and this can be adjusted to various levels of prism power and base direction
36
Prentice's Rule Formula
P = cF P - prismatic effect (∆) c - Decentration of the optical centre of the lens (cm) F - Power of the lens (D) WHEN THE PRINCIPLE MERIDIANS ARE 90 AND 180
37
Decentration Rule for +ve powered lenses
BASE DECENTRATION IS THE SAME AS THE DECENTRATION upwards decentration = base up downwards decentration = base down inwards decentration = base in outwards decentration = base out
38
Decentration Rule for -ve powered lenses
BASE DECENTRATION IS OPPOSITE THE OF THE DECENTRATION upwards decentration = base down downwards decentration = base up inwards decentration = base out outwards decentration = base in
39
Prism Movement Rules
Down and out = Positive Up and in = Negative
40
Prismatic Effect of a Centred Sphero-Cylindrical Lens Known Decentration, so we need to work out the Prism 2ND YEAR
H ∆ = (x sin θ + y cos θ) sin θ . C + xS V ∆ = (x sin θ + y cos θ) cos θ . C + yS x = horizontal decentration in cm: outwards = +ve, inwards = -ve y = vertical decentration in cm: downwards = +ve, upwards = -ve S = sphere power C = cylinder power H ∆ = resultant horizontal prism: +ve = base out, -ve = base in V ∆ = resultant vertical prism: +ve = base down, -ve = base up NOTE : for right eyes θ = 180 – cyl axis
41
Decentration needed to produce required level of Prism Known Prism, so we need to work out the Decentration 2ND YEAR
x = DH - BV / S(S+C) y = AV - BH / S(S+C) A = S + Csin^2 θ B = C sinθ cosθ D = S + C cos2θ Where : S = sphere power C = cylinder power H = required horizontal prism V = required vertical prism θ = 180 – cyl axis for right eyes θ = cyl axis for left eyes
42
Why do we Divide Prism?
One lens may be significantly heavier and thicker than the other (cosmetic reasons)
43
Rules when Dividing Prism
Vertical Prism - the opposite of base UP in one eye is base DOWN in the fellow eye Horizontal Prism - the opposite of base OUT in one eye is base OUT in the fellow eye (and the opposite of base IN in one eye is base IN in the fellow eye)
44
Vergence formula
refractive index of the material currently in (n') / distance to/from a focal point (m)
45
What vergence do diverging rays of light have?
-ve vergence
46
What vergence do converging rays of light have?
+ve vergence
47
What happens to the dioptric value for vergence as a pencil of rays get closer to a focal point?
Dioptric value for vergence increases
48
What happens to the dioptric value for vergence as a pencil of rays get further away from a focal point?
Dioptric value for vergence decreases
49
Formula to calculate the theoretical size of the blur circle
b / a = (k’ – f’) / f’ b - blur circle size a - pupil size k' - axial length of the eye f' - focal length of the eye
50
What happens as a myope switches from CL's to spectacles?
Everything shrinks (minified)
51
What happens as a hyperope switches from CL's to spectacles?
Everything becomes bigger (magnified)
52
Define Spectacle Magnification
The ratio of image size in an eye corrected by a spectacle lens to the image size in an uncorrected eye
53
What are the 2 components of spectacle magnification?
-Shape factor -Power factor
54
What is Shape factor affected by?
Affected by the F1 and the centre thickness of the lens
55
What is Power factor affected by?
Affected by the BVP and where the lens is
56
Formula to calculate spectacle magnification
Spectacle magnification = Shape factor x Power factor
57
How do you calculate Shape factor?
Shape factor = 1 / 1- (t/n' x F1) t - centre thickness of the lens (m) n' - refractive index of lens material F1 - front surface power
58
How do you calculate Power factor?
Power factor = 1 / 1 - (d x BVP) d - back vertex of spectacle lens (m) (assume entrance point is 3mm behind corneal apex) d = BVD + 3 BVP - back vertex power
59
What can you do to the front surface of the lens to increase the magnification?
Use a more curved front surface
60
When would the Power factor remain constant?
-BVP is the same -BVD is the same
61
How can you check if your answers are roughly correct?
Shape factor and Power factor should be close to 1
62
True or false Power factor is less than 1 if the lens is +ve
False Power factor is less than 1 if the lens is -ve
63
What happens to the values of Shape factor and Power factor if you have a -ve value for F1?
Shape factor will be slightly larger than Power factor
64
What happens to the image size and field of view in a hyperope? What does this lead to?
-Image is bigger -Smaller field of view -Leads to a ring scotoma (ring shaped area of blindness)
65
What happens to the image size and field of view in a myope? What does this lead to?
-Image is smaller -Larger field of view -Leads to diplopia (double vision)
66
What a could a potential reason be other than pathology/disease as to why a myope can't see all the way down to the bottom line during refraction?
It may simply be because the spectacles minify images so objects look smaller in size
67
What is anisoconia?
Difference in image size between the 2 eyes, usually due to a very different Rx between the 2 eyes
68
What happens to the magnification if you make a -ve lens thicker?
Magnification increases
69
Formula to calculate the new power after a change in BVD for spectacles/CL's
BVP = F / 1 - xF BVP - power of the lens at the new BVD F - original lens power x - difference in BVD (m) (old BVD - new BVD)
70
What happens to the power of the -ve correcting lens for a myope when the BVD increases?
Increases
71
What happens to the power of the +ve correcting lens for a hyperope when the BVD increases?
Decreases
72
What power should you choose when choosing the correct lens?
-Most minus power -Least plus power
73
Why is spectacle magnification important? What do we need to consider?
-The perceptual changes experienced by a newly corrected ametrope -Drastic changes in refraction following refractive surgery and cataract surgery -Changes experienced when swapping between modes of correction (e.g. the high myope removing their contact lenses and putting on their spectacles) -Px's with anisometropia (huge difficulty in fusing images because of different spectacle magnification effects in each eye)
74
What are the toric surfaces within the eye?
-Front and rear surface of the cornea -Front and rear surface of the lens
75
What will have a greater refractive effect, front or rear surface of the cornea and why?
Front of the cornea will have a greater refractive effect than the rear surface as there is a bigger change for the front (tear film —> cornea) compared to the rear (cornea —> aqueous)
76
Give the formula to calculate the power of a cylindrical lens along an axis other than the principal meridians
Fθ = F.sin^2(θ)
77
How is Fθ = F.sin^(θ) different to Meridional Power = S +C.sin2 θ?
Exactly the same, Fθ = F.sin^2(θ) is used for only a cylindrical lens whereas Meridional Power = S +C.sin2 θ takes into account sphere power as well
78
Give the steps on how to construct a triangle to combine 2 lenses (Stokes construction)
1) Transpose the lenses so that they are in positive sphero-cylindrical form 2) Choose the lens with the smaller numerical axis (if one axis is 180, call this zero) 3) Draw a line to scale (length and axis direction) which represents the first cylinder power (F1); line OA below 4) Draw a second line to scale at an angle to the first line of twice the difference in axis (F2); line AR below 5) Draw a third line to complete the triangle. The length in this line represents the power of the resultant cylinder (C); line OR below 6) Bisect the angle between the first line drawn and the resultant cylinder. The angle between this line and the 180 line is the axis of the resultant cylinder 7) The new sphere power will be (F1 + F2 – C) / 2, plus any spheres from the initial transposition
79
How many lenses can you combine using Stokes construction?
ONLY 2
80
What 3 terms do we divide a Rx into and calculate in order to combine different lenses together that don't have the same principal meridians? (Astigmatic Decomposition)
-M -J180 -J45
81
Formula to calculate M What is M? (Astigmatic Decomposition)
M = S + C/2 M - mean spherical power
82
Why does M = 0 for a JCC lens?
E.g. +0.25/-0.50 M = S + C/2 M = +0.25 + (-0.50/2) = 0 (plano)
83
Formula to calculate J180 What is J180? (Astigmatic Decomposition)
J180 = -0.5C*cos(2A) 2A - 2 x Axis A crossed-cylinder at 90/180
84
Formula to calculate J45 What is J45? (Astigmatic Decomposition)
J45 = -0.5C*sin(2A) 2A - 2 x Axis A crossed-cylinder at 45/135
85
Steps to combine 2 or more sph/cyl lenses that do not have the same principal meridians
1) Calculate M, J180 and J45 for each lens 2) Calculate ∑M, ∑J180 and ∑J45 3) Calculate Resultant Sphere 4) Calculate Resultant Cylinder 5) Calculate Resultant Axis
86
What are all of the components (M, J180, J45) measured in? What does this enable us to do?
All of the components are measured in Dioptres Enables us to combine numerous different lenses
87
Why will the values of J180 and J45 be small?
J180 and J45 are crossed cylinders
88
Formula to calculate Resultant Sphere
Resultant Sphere = ΣM + √[ (ΣJ180)^2 + (ΣJ45)^2 ]
89
Formula to calculate Resultant Cylinder
Resultant Cylinder = -2*√[ (ΣJ180)^2 + (ΣJ45)^2 ]
90
Formula to calculate Resultant Axis
Resultant Axis = 0.5tan-1 (ΣJ45 / ΣJ180)
91
How do you fix the resultant axis when the calculated value is less than 45?
Use the calculated value
92
How do you fix the resultant axis when the calculated value is greater than 45 and less than 135?
Add 90 to calculated value
93
How do you fix the resultant axis when the calculated value is greater than 135?
Add 180 to calculated value
Visual and Applied Optics 1
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