How to find the intersection values?

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);

Answer 1

[Bruno Luong]

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

[GULZAR]

Thank you. And how to show the intersection points...

[Torsten]

xx

at the end of the for-loop.

Answer 2

[Torsten]

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

sol = 1×5

0.425911883383464 0.453366368933051 0.559061333603378 0.580387744533463 0.740288322697614

% 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

sol = 1×5

0.398347393959160 0.476820539375385 0.520624847917834 0.636196969306721 0.680659944575321