This document discusses sign conventions and vergence in optics. It defines sign conventions as choices of plus or minus signs used consistently in physics equations. The Cartesian sign convention for optics is described. Vergence is defined as the curvature of optical wavefronts and can be positive (convergence) or negative (divergence). Types of lens power specification are also outlined, including approximate, back vertex, front vertex, equivalent, and effective power. The document concludes that back vertex power is most commonly used in optics.

1. Sign convention and
vergence
SURAJ SHIL
B.OPTOM 2nd YEAR
RIDLEY COLLEGE OF OPTOMETRY, JORHAT

2. Sign convention
 In physics, a sign convention is a choice of the physical
significance of signs (plus or minus) for a set of quantities, in a
case where the choice of sign is arbitrary.
 "Arbitrary" here means that the same physical system can be
correctly described using different choices for the signs, as
long as one set of definitions is used consistently

3. Cartesian sign convention
 Cartesian means of or relating to the French philosopher René
Descartes—from his Latinized name Cartesius.
1) Light initially propagates from left to right.
2) The origin of the Cartesian coordinate system is at the centre of the
optical component.
3) Distances measured normal to the optic axis are positive above and
negative below.
4) We denote object space distances as l, h, f, and image space distances
as l ', h', f '.
5) Acute angles are positive when produced by anticlockwise rotation from
the optic axis, and negative when produced by clockwise rotation.

4. Representation

5. In lenses…

6. Vergence
 A vergence is the simultaneous movement of both eyes in
opposite directions to obtain or maintain single binocular
vision.
 When a creature with binocular vision looks at an object, the
eyes must rotate around a vertical axis so that the projection
of the image is in the centre of the retina in both eyes.

8. Vergence
 In optics, vergence describes the curvature of optical
wavefront in a specific distance from the origin or focus
 Vergence, L = n/I ; where, n = refractive index
I = distance between the point
and reference plane

9. Types
i. Convergence or Positive vergence
ii. Divergence or Negative vergence

10.  Wavefronts propagating toward a single point yield positive vergence. This
is also referred to as convergence since the wavefronts are all converging
to the same point of focus.
 Contrarily, wavefronts propagating away from a single source point give
way to negative vergence. Negative vergence is also called divergence

11. Vergence amplification effect
 The increase in the divergence of light that occurs when an
afocal telescope is used to view an object at finite distance is
referred as Vergence Amplification Effect
 The value of the vergence amplification effect is the square of
the magnification brought about by the telescope in question

12. Contd…
 Bailey showed that if a 3x afocal telescope is used to view an
object at a distance of 4m, the vergence of light rays entering
the objective (0.25D) is increased by a factor of 9, so light
emerging from the eyepiece has a vergence of 9(0.25) or 2.25
D, thus requiring 2.25D of accommodation on the part of the
wearer

13. Power
 Refracting power is defined as the change in vergence that
occurs when light passes through a refractive media
 The unit used for specifying the power of a spectacle lens is
the diopter, abbreviated by the letter D

14. Power specification
 A number of methods can be used to specify the power of an
ophthalmic lens
1) Approximate power
2) Back vertex power and Front vertex power
3) Equivalent power
4) Effective power

15. Approximate power
 Also known as nominal power
 According to it the power of a lens is specified in terms of its
front and back surface powers without regard to its thickness
 The approximate power of an ophthalmic lens is given by the
simple formula, FA = F1 + F2
where, F1 and F2 are the front and back surface
powers as measured by the lens measure(lens clock)

16. Front vertex power
 Front vertex power (also called neutralizing power) is defined
as the negative reciprocal of the reduced distance from the
front pole of the lens to its primary focal point
 The front vertex power of a lens can be given with the
formula,
FN = F1 + F2 + F2
2
t/n

17. Back vertex power
 The back vertex power of an ophthalmic lens is defined as the
reciprocal of the reduced distance from the back pole of the
lens to the secondary focal point
 The back vertex power of a lens can be given by,
FV = F1 + F2 + F1
2
t/n

18. Comparison,
 Given a lens for which F1 = +6.00D, F2 = -7.00D, t = 2.00 mm
and n=1.523, find FA, FV and FN
For approximate power,
FA = F1 + F2
For back vertex power,
FV = F1 + F2 + F1
2
t/n
For front vertex power,
FN = F1 + F2 + F2
2
t/n

19.  FA = -1.00 D
 FV = -0.95 D
 FN = -0.94 D

20. Equivalent power
 The focal length of the thin lens that will produce an image
size and an image position similar to those produced by a
system is called equivalent focal length
 The reciprocal of the equivalent focal length in meters is
defined as the equivalent power
 It can be calculated as,
FE = F1 + F2 – cF1F2,
where c = t/n

21. Effective power
 The effective power of a lens may be defined as the ability of
the lens to focus parallel rays of light at a given plane
 The term effective power is also used to indicate the change
in lens power required if a lens is moved from one position to
another in front of the patient’s eye
 Given by the formula,
FB = FA / (1-dFA)

22.  Example:

23. Conclusion
 Of all the methods of power specification only back vertex
power is used routinely by optical laboratories and
practitioners
 It is convenient to use back vertex power because ophthalmic
lenses are placed in the spectacle plane at a fixed distance
from the cornea and back vertex power gives the effective
power of the lens in the spectacle plane

24. References
 Clinical Optics, page no. 2,3, 53-61
 Theodore Grosvenor, Primary Care Optometry, 5th edition, Page no.440
 https://en.wikipedia.org/wiki/Sign_convention
 https://www.st-andrews.ac.uk/~bds2/optics/cartesian.html
 https://www.en.eyebrainpedia.com/vergence
 http://hydrogen.physik.uni-
wuppertal.de/hyperphysics/hyperphysics/hbase/geoopt/vergence.html

25. THANK YOU