Sags and Edge Thickness

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

Define lens curvatures

cv = [0.0104227 -0.0406946]

cv =

    0.0104   -0.0407

Define a range of heights.

ap = 9;
y = linspace(-ap,ap,81);

Define the center thickness

th = 3.0486;

Calculate the sags

$z = \frac{cr^2}{1+\sqrt{1-(cr)^2}}$

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

Draw the two sides of the lens

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

Edge thickness

eth = th - sag(ap,cv(1)) + sag(ap,cv(2));
fprintf('edge thickness %g\n',eth);

edge thickness 0.918096

lens shape factor

$B = \frac{c_1+c_2}{c_1-c_2}$

shape = (cv(1)+cv(2))/(cv(1)-cv(2));
fprintf('shape factor %g\n',shape);

shape factor -0.592205