This document discusses the optics of contact lenses. It begins with a brief history of contact lenses and an introduction to basic optics concepts for thick lenses. It then covers various optical properties of contact lenses like vertex distance correction, magnification, accommodation, convergence, and aberrations. Key advantages of contact lenses are discussed, such as producing a more natural retinal image size for myopes and hyperopes compared to spectacles. Factors affecting spectacle and contact lens magnification are also presented.

1. OPTICS
OF
CONTACT LENS
Moderator Presenter
Dr. Sanjeev Bhattarai Aayush chandan

2. Presentation Layout
• Introduction
• Basic optics
• Various optical properties of CL
• Advantage & Disadvantages Of CL
• References

3. What is contact lens ?
• It is an artificial device placed on cornea or sclera for optical or therapeutic
purpose.

4. History of contact lens
• In 1508 , Leonardo da vinci first conceived & sketched prototypes of
modern contact lens
• Experimented by neutralizing his own refractive error by placing his face in
a container of water

5. Basic optics
• Although thin in appearance , CL are treated in geometrical optics as a thick
lens
• Unlike thin lenses , the refraction of light as it passes through the thickness
of the lens must be taken into consideration
• Thin lens
𝐹𝒕𝒉𝒊𝒏 = 𝐹1 + 𝐹2
• Thick lens
𝐹𝒕𝒉𝒊𝒄𝒌 = 𝐹1 + 𝐹2 −
𝐭
𝐧
(𝐹1 ∗ 𝐹2)
𝐹 𝒔𝒖𝒓𝒇𝒂𝒄𝒆 =
𝑛′ − 𝑛
𝑟 𝒔𝒖𝒓𝒇𝒂𝒄𝒆

6. Conjugate planes
• Conjugate planes are planes perpendicular to the optical axis whose
positions are related to each other by the image forming properties of the
lens.

7. Principal plane
• The principal planes are two hypothetical planes in a lens system at which
all the refraction can be considered to happen .
• For a given set of lenses & separations , the principal planes are fixed & do
not depend upon the object position

8. Back vertex power
• The true focal lengths (f’ & f) are measured from the principal planes .
• Since these planes are theoretical constructs their locations are not obvious .
• Clinically it is not practical to measure true focal lengths of either contact lens or
specs.
• In practice we measure the position of second principal focus from the back
vertex of the lens since this is accessible .The power so measured is the Back
Vertex Power (BVP)

10. The Effectivity Relationship
• Vergence at any point is the inverse of the distance from the point to which
it is converging or from which it is apparently diverging .
• When light is travelling in a medim other than air , the vergence is n/d i.e
the reduced vergence .
Vergence at D = 1/l
Vergence at D’= 1/l-d = L/1-dL

11. • So from the effectivity relationship we can have
• Back vertex power
• Fv’=
𝐹1
1−
𝑡
𝑛
𝐹1
+ 𝐹2
• Fv’=
𝐹 𝑒𝑞
1−
𝑡
𝑛
𝐹1
Where ,
Feq = F1+F2-(t/n)F1F2

12. Front vertex power
• Also called as neutralizing power
• FVP can be calculated in a similar manner to that of BVP
FV =
𝐹2
1−
𝑡
𝑛
𝐹2
+ F1
FV =
𝐹𝑒𝑞
1−
𝑡
𝑛
𝐹2
• Used when specifying the power of haptic lens because the depth of a
scleral shell may prevent the back vertex from touching the focimeter stop

13. Optics of contact lens
Various optical properties of contact lens include
• Vertex distance correction
• Magnification
• Accommodation
• Convergence
• Tear lens
• Field of vision
• Aberration
• Neutralization of astigmatism
• Over refraction

14. Vertex Distance Correction
• Vertex distance is the distance between back surface of lens & front surface of
cornea .
• Formula for vertex correction is
FCL=
𝐹 𝑆𝑃
1−𝑑𝐹𝑆𝑃
• If distance(d) is not measured an assumption based on wearer’s anatomy can be
made
• In Asian people , figures of 10-14 mm generally apply
• For Caucasians value of 12-15 mm are more likely

16. Spectacle magnification
• Concerns the change in the retinal image size of a single eye brought about
by a correcting lens(either spectacle lens or a contact lens)
• SM =
𝑅𝑒𝑡𝑖𝑛𝑎𝑙 𝑖𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑒𝑦𝑒
𝑅𝑒𝑡𝑖𝑛𝑎𝑙 𝑖𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑢𝑛𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑒𝑦𝑒
• Mathematically,
• SM =
1
1−
𝑡
𝑛
𝐹1
(
1
1−ℎ𝐹𝑉
)
Where,
F1=power of front surface of lens
Fv=BVP of composite lens
t= lens thickness
n=index of refraction of lens material
h=distance from back vertex of lens to entrance pupil of
eye

17. • Spectacle magnification is always greater than unity for a plus lens & less
than unity for a minus lens(for both spectacle and CL)
• Although the amount of magnification is different for a CL than that for
spectacle lens because of much shorter distance between lens & entrance
pupil of the eye

18. Contact lens magnification
• Contact Lens Magnification is the ratio of the image sizes in an ametropic
eye corrected by a contact lens (CL) and a spectacle lens (SL).
• CLM =
𝐶𝐿 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒
𝑆𝐿 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒
• Realistic since focused image are used in both the numerator and
denominator

19. Spectacle vs Contact Lens
• Image size in any optical system is directly
proportional to the focal length of the system
(or inversely proportional to lens power).
• So , in hyperopia fCL<fSL(shorter by vertex
distance)consequently , Image size is smaller
when CL are worn.
• In Myopia , fCL>fSL , image size is larger

20. • In comparing spectacle and contact lens image sizes:
CLM = 1 -d FSP
Examples with d = 14 mm
+ 10.00 D, CLM = 0.86
- 10.00 D, CLM = 1.14
• With contact lenses, hyperopes experience a smaller image size than they would
with spectacles of equivalent power.
• Similarly, myopes experience a larger image size than they would with spectacles of
equivalent power.
• Both of these outcomes are desirable and together constitute perhaps the biggest
single advantage of contact lenses over spectacles.

21. Relative spectacle magnification
• Defined as the ratio of the retinal image size(for an object at infinity) of the
corrected ametropic eye to that of standard emmetropic eye.
• RSM =
𝑖𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒 𝑓𝑜𝑟 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑎𝑚𝑒𝑡𝑟𝑜𝑝𝑖𝑐 𝑒𝑦𝑒
𝑖𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒 𝑓𝑜𝑟 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑚𝑚𝑒𝑡𝑟𝑜𝑝𝑖𝑐 𝑒𝑦𝑒
• To compare retinal image size of one eye with that of another eye.
• RSM =
𝑓′
𝐸
𝑓′
𝑆𝑇
=
𝐹 𝑆𝑇
𝐹 𝐸

22. RSM in Refractive ametropia
• If the source of the ametropia is assumed to be refractive
• RSM = 1 + d2FSP
• With Spectacles (d2 ≈ d = vertex distance): [RSM ≠ unity]
• With Contact Lenses, d2 = 1.55 mm. In this context 1.55 mm is treated as being
negligible (≈ 0). [RSM ≈ unity]
• Clearly, if anisometropia results from ametropia (unilateral or bilateral) which
is refractive in origin, contact lenses would be the correction of choice
because they produce negligible differences between the corrected image
size and the normal emmetropic image size

23. RSM in Axial ametropia
• RSM = 1 - g F SP
• With Spectacles (g ≈ 0 i.e. d2 ≈ - f ) [RSM ≈ UNITY]
• With Contact Lenses g = feye - (d + 1.55) [RSM ≠ UNITY]
Knapp’s Rule
• For axially ametropic eye , if the correcting lens is placed so that its secondary
principal point coincides with anterior focal point of the eye , the size of retinal
image is same as if it were standard emmetropic eye
• Clearly, if anisometropia results from ametropia (unilateral or bilateral) which is
axial in origin, spectacles would be the correction of choice

24. How do SM, CLM and RSM Relate to One
Another ?
• SM is a real-world comparison of corrected (focused) and uncorrected
(blurred) retinal image sizes
• CLM is a more realistic comparison of contact lens corrected versus
spectacle lens corrected retinal image sizes
• RSM is a hypothetical magnification comparing image sizes in a corrected
ametropic eye and a theoretical emmetropic schematic eye.

25. Accommodation
Spectacle Refraction VS ocular Refraction
• The power of the correcting lens , specified at the spectacle plane is termed
spectacle refraction
• The power of the correcting lens , specified at the first principal plane of the
eye is termed ocular Refraction
+10D -10D
Spectacle refraction = +10D Spectacle Refraction = -10D
Vertex Distance = 15mm Vertex Distance = 15mm
Secondary focal length = 10cm-
1.5cm=+8.5cm
Secondary focal length = -10cm-
1.5cm=-11.5cm
Ocular Refraction =
1
+0.085
=+11.76D Ocular Refraction =
1
−0.115
= -8.70D

26. Spectacle accommodationVS ocular
accommodation
• For sake of convention , accommodation is usually considered to take place at
the spectacle plane .(spectacle accommodation)
• However because it represents a change in ocular refraction , accommodation
actually takes place at the first principal plane (ocular accommodation)
• The amount of ocular accommodation required of an eye can be determined
by the use of formula
ocular accommodation =Vd -Vn
• For emmetrope,
Vd =
1
𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑦
= 0
Vn=
1
−0.40−0.015
= -2.41D (0.09D less than 2.50D for spectacle plane)

27. +10D -10D
Ocular refraction (Vd)= +11.76D Ocular refraction (Vd)=-8.70D
Vergence of light at the spectacle plane
= -2.50+10=+7.50D
Vergence of light at the spectacle plane
= -2.50-10=-12.50D
Distance from spectacle plane to image
= 1/+7.50=+0.133m
Distance from spectacle plane to image
= 1/-12.50=-0.08m
Distance from principal plane to image
=+0.133-0.015=+0.118m
Distance from principal plane to image =
-0.08-0.015=-0.095m
Vn=
1
+0.118
= +8.47D Vn=
1
−0.095
= −10.53𝐷
Ocular accommodation =Vd-Vn = +11.76-
(+8.47)=+3.29D
Ocular accommodation =Vd-Vn = -8.70-(-
10.53)=+1.83

28. • The 10D hyperope , therefore must accommodate about 1D more than
emmetrope & 10D myope needs to accommodate about 0.50D less than
emmetrope
• Because a contact lens fits on the cornea rather than about 13mm in front
of it and therefore is less than 2mm in front of the first principal plane of
the eye , the 10D hyperope has to accommodate less while wearing CL
than while wearing spectacles and the 10D myope has to accommodate
more while wearing CL than while wearing Spectacle

29. In summary
• Spectacle wearing myopes accommodate less than spectacle wearing
hyperope
• With CL wear , the accommodation required in ametropia is approximately
the same as emmetrope
• Accommodative demand of a myope is greater in CL than with Spectacle
• Accommodative demand of a hyperope is greater with spectacle than with
CL

30. Incipient presbyopia
• If a myope is switched from spectacles to contact lenses the change may
precipitate the need for a near correction
• If a hyperope is switched from spectacles to contact lenses the need for a
near correction may be postponed

31. Convergence
• Monocular convergence =
ℎ(𝑖𝑛 𝑐𝑚)
𝑞 (𝑖𝑛 𝑚)
• for PD=64mmVD=14mm CR=13.5mm
Where h=IPD/2
q= distance from the plane of
fixation to the centre of rotation of
the eye
CL Spectacle
-5.00D 14.97 13.26
Plano 14.97 14.97
+5.00D 14.97 17.18

32. • A hyperope wearing CL converges less than when wearing spectacles
because of the BO prismatic effect induced by speactacles acting as an
exercising prism which forces more convergence than vertex distance
would suggest. Since CL moves with the eye, no such prismatic
consideration applies
• A myope wearing CL converges more than wearing Spectacle because of BI
relieving prism effect & eye converges less thanVertex distance would
suggest .

34. •
Patient Change in accommodative
demand
Change in accommodative
convergence and phoria (at
near vision)
Change in prismatic effects
and phoria(at near vision)
High myopia with exophoria
at near(low AC/A ratio)
Increase Increase;
decreased exophoria
Lack of BI effect;
*increased exophoria
High myopia with esophoria
at near(high AC/A ratio)
Increase Increase ;
*increased esophoria
Lack of BI effect;
decreased esophoria
High hyperopia with
exophoria at near(low AC/A
ratio)
Decrease Decrease ;
increased exophoria
Lack of BO effect ;
*decreased exophoria
High hyperopia with
esophoria at near (high AC/A
ratio)
Decrease Decrease ;
*decreased esophoria
Lack of BO effect ;
increased esophoria

35. The tear lens
• Tear lens is formed between the posterior surface of CL & anterior surface
of cornea
• SCL conforms to the corneal curvature & forms a plano tear lens
• If RGP is used , ‘tear lens’ depends on the relationship between the
curvature of the lens back surface & cornea & to lesser extent , the
material’s rigidity
BC equal to K reading : plano power tear lens
BC steeper than K : plus power tear lens
BC flatter than K : minus power tear lens

37. Tear lens power with rigid lenses
• A rule of thumb can be derived for tear lens under rigid lenses
• ntear = 1.336 nlens = 1.490
nair = 1.000 r0=7.80mm
flatter(r=7.85mm) Steeper(r=7.75mm)
• For convenience consider that CL &TL are separated by thin layer of air
TL front surface power (FSTears)=
1.336−1.000
0.0078
= +43.076923
For (r=7.85) FSTear = +42.802548 for (r=7.75mm) FSTear = +43.354839
∆ = -0.274375D ∆ = +0.277916D

38. Rule of thumb
• ∆0.05mm in BOZR ≈ ∆0.25D in BVP required to offset ∆ in tear lens power

39. FOV
• The pheripheral FOV is the field of view for steadily fixating eye ,
subtended at the entrance pupil & is given by equation
Tan Φ = y(E-F)
• Macular FOV is the field of view for moving eye , subtended at centre of
rotation of eye
Tan θ = y(S-F)
where
Φ=one-half of the angular FOV
Θ= one-half of the angular FOV
Y= one-half of the lens aperture (in m)
E= the vergence of light at the entrance pupil of the
eye
S=the vergence of light at the centre of rotation of
eye
F= the power of the correcting lens

40. • For a spectacle lens of aperture 50mm andVD=15mm from entrance pupil
• For a CL of aperture 7mm andVD=3mm from entrance pupil
• In both examples above , the peripheral FOV is about 20° smaller with a CL than
with Spectacle
Spectacle lens Contact lens
+5D 2Φ=114.06° 2Φ=97.93°
-5D 2Φ=121.66° 2Φ=99.63°

41. • Although these result could vary somewhat depending onVD of spectacle
lens & aperture size of spectacle lens & CL , it is apparent that a CL doesn’t
necessarily provide a longer peripheral FOV than spectacle lens
• The FOV is larger for a CL wear is not the peripheral FOV but Macular FOV
• The macular FOV can be shown to be larger for minus lens than plus lens

42. Field limitation
• .
Hyperopia Myopia
The ring scotoma is produced by
the difference between the field
limitations imposed by the
frame/lens combination & optics of
plus lens.
The ring diplopia is produced by
the difference between the field
limitations imposed by the
frame/lens combination & optics of
plus lens
As CL moves with the eye , no such
limitation or scotoma results
As CL moves with the eye no such
limitation or diplopia results

43. Aberration
• Because a CL wearer always looks through a point at or near optical centre
of the lens , Chromatic aberration (longitudinal &Transverse) doesn’t
present a problem
• The aberration of Spherical aberration & Coma occur only for large aperture
optical system. As with spectacle lenses , aberration do not present a
problem for CL of moderate power because eye looks through only a small
position of lens

44. • The aberration of Oblique astigmatism & Curvature of Image occur when a
narrow pencil of light from an object passes obliquely through spherical
surface . Because CL fits the eye in such a way that foveal line of sight
always passes through a point at or near the optical centre of lens ,
aberration do not present a problem for CL wearer
• Distortion result as gradual change in magnification brought about by the
lens from centre towards periphery . Because eye always fixates through
the centre of CL & pupil of eye is very small , distortion is not apt to be
problem for CL wearer

45. Neutralization of astigmatism
• Since refractive indices of the cornea & tear are not vastly different , the
effectiveness of optical interface between two is much reduced
• If an astigmatic cornea is fitted with RGP ,tear lens is sphericalized by back
surface of lens
• It is usually difficult to fit spherical lenses on cornea with 3D of corneal
astigmatism.
• Some claim that 2D is a more realistic upper limit
• If astigmatism is to be corrected with SCL, toric lenses must be used

46. Approximately 90% of corneal astigmatism is neutralized
by spherical RGP lenses

47. Over Refraction
• With RGP
Oc Rx = BVP trail + PTL + Over Rx
• With SCL
Oc Rx = BVPTrail + Over Rx

48. Reasons for Discrepancies
• Failure to correct for vertex distance of spectacle Rx when deriving the ocular
Rx
• Failure to correct the over-Rx for vertex distance when it is > ±4D
• K readings only represent the central zone (approximately 3 mm) and give no
indication of the shape of the periphery.
• Tear lens power varies slightly with K readings
• Trial lens BVP may be incorrect
• Subjective over-Rx is incorrect
• BOZR of the trial lens is incorrect
• Trial lens is decentred and/or tilted.

49. • Trial lens flexure in situ for both rigid and soft lenses can mislead the
practitioner
• Corneal molding by the lens
• Corneal shape not spherical or spherocylindrical
• Variable toric tear lens due to lens movement,decentration, tilting, rotation
• Environment-induced changes in a thick, soft trial lens

50. Advantages and Disadvantages of CL
Advantages Disadvantages
No astigmatism of oblique pencils. Lens decentration produces ‘ghosting’ or flare from
the peripheral zone of the lens
No distortion When a toric lens rotates, a toric over-refraction
and decreased vision may result.
No chromatic aberration Moving or generally unstable lenses may produce
disturbances of vision
No limitations on the field of view In axial ametropia, usually spectacles are better
suited
No spectacle frame diplopia. (Myopia).
No spectacle frame scotoma. (Hyperopia).
No prismatic imbalance in anisometropia
Corneal irregularities/astigmatism reduced by
90%.

51. References
• IACLE module
• Clinical Optics ; Fannin & Grosverner
• Internet