Page 110 - The Indian Optician Digital Edition May-June 2023
P. 110

THE SAG FORMULA





                                                                                             – PART 2









                                             Dr Prof Mo Jalie, DSc, SMSA, FBDO (Hons), SLD, Hon FCGI Hon FCOptom,
                                             MCMI, is a Visiting Professor of Optometry at the University of Ulster in
                                             Coleraine, and at the post-graduate facility at Varilux University. He served for
                                             nine years as Head of Department of Applied Optics at City
                                             & Islington College, where he taught optics, ophthalmic lenses and
                                             dispensing. He is a recognised international authority on spectacle lens
                                             design and has written several books including Principles of Ophthalmic
                                             Lenses. His most recent book, Ophthalmic Lenses & Dispensing was
                                             translated into Russian. He has authored over 200 papers on ophthalmic,
                                             contact and intra-ocular lenses, and on dispensing; and is a consultant editor
                                             to The Optician (UK) and technical editor to The Indian Optician journal.
                                             He holds patents for aspheric spectacle and intra-ocular lenses. Jalie is a
                                             past-chairman of the Academic Committee of the Association of British
                                             Dispensing Opticians, and was the first Chairman of the Faculty of Dispensing
                                             Opticians. He is the ABDO representative on the BSI committees on
                                             ophthalmic lenses and spectacle frames and a past member of the Education
                                             Committee of the General Optical Council. In 1998 Jalie was thrice honoured:
                                             he was made Honorary Fellow of the British College of Optometrists, a Life
                                             Fellow of the Association of British Dispensing Opticians, and in December of
                                             that year he was granted the Max Wiseman Memorial Research Medal.
            Dr Prof Mo Jalie





               he first part of this article on lens thickness   z = y  / r + √(r  – y ) = 30  / 99.6 + √ 99.6  - 30

                                                                                                   2
                                                                                                        2
                                                                                    2
                                                                  2
                                                                           2
                                                                              2
               gave various versions of the formula from      = 4.63mm.
          Twhich the sag of a spherical surface could
          be calculated. For convenience, these formulae      Trigonometric solution 1: sin θ = y / r = 30 / 99.6
          are repeated here, all formulae will give the       = 0.3012, so, angle θ = 17.53°.
          same result for a curve of specified diameter       z = r (1 - cos θ) = 99.6 (1 - cos 17.53) = 4.63mm.
          (2y) and radius (r). For the benefit of students,
          some examples showing how lens thickness is         Trigonometric solution 2: sin 2U = y / r
          calculated for various forms of lens.               = 30 / 99.6 = 0.3012, so, angle U = 8.765°.
                                                              z = y tan U = 30 tan 8.765 = 4.63mm.
             As a reminder of the use of the sag formula
          to calculate the sag of a curve, the sag of a 5.00     It is immaterial which form of the sag
          Dioptre curve (F) worked on CR 39 material of       formulae the reader prefers but for reasons
          refractive index, (n) 1.498, at a diameter of 60mm   which will emerge later, the author’s preferred
          is given. First, the radius of curvature of the     form is the alternate quadratic solution given as
          surface, r, must be found from r = 1000(n - 1)/F =   solution two in the above four possibilities.
          1000(1.498 - 1)/5 = 99.6mm.
                                                              CALCULATION OF LENS THICKNESS
          Quadratic solution: z = r - √(r  – y )
                                          2
                                      2
          z = 99.6 - √(99.62 - 302) = 4.63mm.                    The thickness of any given lens is found by
                                                              calculating the sag of its curved surface (or,
          Alternate quadratic solution:                       sags of each surface if the lens has two curved


      106 | THE INDIAN OPTICIAN | MAY-JUNE 2023                                                           LENS TALK
   105   106   107   108   109   110   111   112   113   114   115