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

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