problem in plot while loop

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shiv gaur
shiv gaur on 16 Feb 2022
Commented: shiv gaur on 16 Feb 2022
k0=(2*pi/0.6328)*1e6;
t2=1.5e-6;
n1=1.512;n2=1.521;n3=4.1-1i*0.211;
n4=1;
m=0;
x=1.512;
t3=1e-9:1e-6;
k1=k0*sqrt(n1^2-x^2);
k2=k0*sqrt(n2^2-x^2);
k3=k0*sqrt(n3^2-x^2);
k4=k0*sqrt(n4^2-x^2);
tol = 1e-12;
n = 1;
while 1
x_new =-(k2)*t2+atan(k1/1i*k2)+atan((k3/k2)*tan(atan(k4/1i*k2)-k3*t3))+m*pi;
if abs(x_new-x) < tol, break; end
x =x_new;
k1=k0*sqrt(n1^2-x^2);
k2=k0*sqrt(n2^2-x^2);
k3=k0*sqrt(n3^2-x^2);
k4=k0*sqrt(n4^2-x^2);
n=n+1;
end
pl plot graph between t3 vs x_new
where x_new is the root of the equation
  8 Comments
shiv gaur
shiv gaur on 16 Feb 2022
k0=(2*pi/0.6328)*1e6;
t2=1.5e-6;
n1=1.512;n2=1.521;n3=4.1-1i*0.211;
n4=1;
m=0;
x=1.512;
t3=1e-9:1e-6;
k1=k0*sqrt(n1^2-x^2);
k2=k0*sqrt(n2^2-x^2);
k3=k0*sqrt(n3^2-x^2);
k4=k0*sqrt(n4^2-x^2);
tol = 1e-12;
n = 1;
while 1
x_new =-(k2)*t2+atan(k1/1i*k2)+atan((k3/k2)*tan(atan(k4/1i*k2)-k3*t3))+m*pi;
if abs(x_new-x) < tol, break; end
x =x_new;
k1=k0*sqrt(n1^2-x^2);
k2=k0*sqrt(n2^2-x^2);
k3=k0*sqrt(n3^2-x^2);
k4=k0*sqrt(n4^2-x^2);
n=n+1;
end
% is nothing that is edited code not able to plot help using while loop x is the root of the equation xnew is the transedental equation

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Accepted Answer

Jan
Jan on 16 Feb 2022
k0 = 2 * pi / 0.6328 * 1e6;
t2 = 1.5e-6;
n1 = 1.512;
n2 = 1.521;
n3 = 4.1-1i*0.211;
n4 = 1;
m = 0;
x = 1.512;
t3 = 1e-9; % ??? :1e-6;
tol = 1e-12;
n = 1;
while 1
k1 = k0 * sqrt(n1^2 - x^2);
k2 = k0 * sqrt(n2^2 - x^2);
k3 = k0 * sqrt(n3^2 - x^2);
k4 = k0 * sqrt(n4^2 - x^2);
x_new = -k2 * t2 + atan(k1/1i*k2) + ...
atan((k3/k2) * tan(atan(k4/1i*k2) - k3*t3)) + m*pi;
if abs(x_new-x) < tol || n > 1e4, break; end
x = x_new;
n = n + 1;
end
n
The formula does not converge.
  2 Comments
shiv gaur
shiv gaur on 16 Feb 2022
why this is not converging where x is the root of function x_new

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