This document discusses sagittal depth, which is the height or depth of a segment of a circle. It provides formulas for calculating the edge thickness (e) of different lens types based on the total thickness (t) and sagittal depth(s) of the lens surfaces. Formulas are given for plano-convex, biconvex, plano-concave, biconcave, positive meniscus and negative meniscus lens configurations. Diagrams illustrate the lens parameters and how they relate mathematically.

1. Lens thickness
OPTOM.ASKAR.PK

4. Sagittal depth

6. Sagittal depth
 Sagittal depth or sag is the height or
depth of a given segment of a circle.
 If both the sag of a lens surface and the
refractive index of a lens material are
known the surface power may be
calculated.

8. A
PQ
C
O

9. Deriving sag formula
 Cord length PQ represent the diameter of
the plano-convex lens
 Edge thickness is zero
 Half of the PQ =y, PQ= 2y
 AO= S ?
 From this picture s= cA- co
 Since CA =r
 S= r-CO CO= ?

10. Using Pythagoras theorem
 ΔCOQ CO² = CQ² - QO²
CO² = r²- y²
CO = √ r²- y²
𝒔 = 𝒓 − √𝒓² − 𝒚²

11. Biconvex lens
𝑡 = 𝑒 + 𝑠1 + 𝑠2
e= t – (s1 + s2)
s1
s2
e

12. Plano convex lens
 t= e+s
 e= t- s
s1
e

13. Positive meniscus
 t= s1- s2+e
 e= t- (s1-s2)

14. biconcave
 e= t+s1=s2
 t= e- (s1+s2)
t
s2
s1

15. Plano concave lens
e= t+ s
t= e-s t
es

16. Negative meniscus
 e= s1-s2+ t
 t= e -(s1-s2)

19. THANK YOUUU