How to find the intersection values?
3 views (last 30 days)
Show older comments
How to find the intersection values of line(black) and the curve(blue)
clc
close all
d1 = 0.4;d2 = 0.6;d = d1 + d2;
n1 = sqrt(12);n2 = 1;
lambda = linspace(400e-3,800e-3, 100000);
D1 = (2*pi*n1*d1)./lambda;D2 = (2*pi*n2*d2)./lambda;
RHS = cos(D1).*cos(D2) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1) .*sin(D2);
plot(lambda,RHS)
hold on
yline(-1);
hold off
hold on
yline(1);
0 Comments
Accepted Answer
Bruno Luong
on 17 Aug 2023
d1 = 0.4;d2 = 0.6;d = d1 + d2;
n1 = sqrt(12);n2 = 1;
lambda = linspace(400e-3,800e-3, 100000);
D1 = (2*pi*n1*d1)./lambda;D2 = (2*pi*n2*d2)./lambda;
RHS = cos(D1).*cos(D2) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1) .*sin(D2);
plot(lambda,RHS)
hold on
for yx = [-1 1]
yline(yx);
ys = RHS-yx;
i = find(ys(1:end-1).*ys(2:end) <= 0);
% linear interpolation
i1 = i; ss1 = ys(i1);
i2 = i1 + 1; ss2 = ys(i2);
w = ss2./(ss2-ss1);
xx = w.*lambda(i1) + (1-w).*lambda(i2);
plot(xx, yx+zeros(size(xx)), 'rx')
end
More Answers (1)
Torsten
on 17 Aug 2023
format long
d1 = 0.4;d2 = 0.6;d = d1 + d2;
n1 = sqrt(12);n2 = 1;
D1 = @(lambda)(2*pi*n1*d1)./lambda;D2 = @(lambda)(2*pi*n2*d2)./lambda;
RHS = @(lambda)cos(D1(lambda)).*cos(D2(lambda)) - 0.5*(n1^2+n2^2)/(n1*n2) * sin(D1(lambda)) .*sin(D2(lambda));
% Case -1
start = [0.42,0.45,0.56,0.59,0.72];
offset = -1;
rhs = @(lambda) RHS(lambda)-offset;
for i = 1:numel(start)
sol(i) = fsolve(rhs,start(i),optimset('Display','none'));
end
sol
% Case 1
start = [0.4,0.47,0.52,0.63,0.67];
offset = 1;
rhs = @(lambda) RHS(lambda)-offset;
for i = 1:numel(start)
sol(i) = fsolve(rhs,start(i),optimset('Display','none'));
end
sol
0 Comments
See Also
Categories
Find more on Interpolation in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!