Sags and Edge Thickness

Find the shape of the lens and the edge thickness using formulas for the sag of a spherical surface.

Sag of Spherical Surface

Matlab code for sag calculation

function z = sag(r,c)
%SAG	The sag function (for spherical surfaces).
%	Z = SAG(R,C)
%
%        C is the curvature (1/radius_of_curvature)
%        R is the radius at which sag is to be evaluated.

	z = c*(r.^2)./(1+sqrt(1-(c*r).^2));

Example

Define lens curvatures:

>> cv = [0.0104227 -0.0406946]

cv =

    0.0104   -0.0407

Define a range of heights:

>> ap = 9;
>> y = -ap:ap;

Define the center thickness:

>> th = >> 3.0486;

Calculate the sags:

>> z1 = sag(y,cv(1));
>> z2 = sag(y,cv(2));

Draw the two sides of the lens:

>> plot(z1,y)
>> hold
>> plot(z2+th,y)
>> axis equal
>> axis([-10 10 -10 10])

Edge thickness

Calculate edge thickness using following formula:

>> th - sag(ap,cv(1)) + sag(ap,cv(2))

ans =

    0.9181

Maintained by John Loomis, last updated 1 Oct 1997