Sign convention

sign convention in relation to maths or physics and also for optometric educational purposes

1. Sign convention and vergence SURAJ SHIL B.Optom 2 nd 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 .

7. 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

8. Types Convergence or Positive vergence Divergence or Negative vergence

9. 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

10. 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

11. 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

12. 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

13. Power specification A number of methods can be used to specify the power of an ophthalmic lens Approximate power Back vertex power and Front vertex power Equivalent power Effective power

14. 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, F A = F 1 + F 2 where, F1 and F2 are the front and back surface powers as measured by the lens measure(lens clock)

15. 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, F N = F 1 + F 2 + F 2 2 t/n

16. 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, F V = F 1 + F 2 + F 1 2 t/n

17. Comparison, Given a lens for which F 1 = +6.00D, F 2 = -7.00D, t = 2.00 mm and n=1.523, find F A , F V and F N For approximate power, FA = F1 + F2 For back vertex power, F V = F 1 + F 2 + F 1 2 t/n For front vertex power, F N = F 1 + F 2 + F 2 2 t/n

18. F A = -1.00 D F V = -0.95 D F N = -0.94 D

19. 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, F E = F 1 + F 2 – cF 1 F 2, where c = t/n

20. 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, F B = F A / (1-dF A )

21. Example:

22. 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

23. References Clinical Optics, page no. 2,3, 53-61 Theodore Grosvenor, Primary Care Optometry, 5 th 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

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