problem in plot while loop

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

[Sajid Afaque]

can u explain your problem in little detail

and i think equation in line number 18 needs to be cross checked

 x_new =-(k2)*t2+atan(k1/%i*k2)+atan((k3/k2)*tan(atan(k4/%i*k2)-k3*t3))+m*pi;

Note : always update your code under code section

[shiv gaur]

x_new =-(k2)*t2+atan(k1/%i*k2)+atan((k3/k2)*tan(atan(k4/1i*k2)-k3*t3))+m*pi; I have edit

code is correct so pl plot

[KSSV]

@shiv gaur If code is correct why you are unable to plot?

[shiv gaur]

why it is not ploting I am using this type

[Jan]

You code does not conatin any command for plotting. Why do you expect, that there is a graphical output?

What is the purpose of:

t3=1e-9:1e-6

This is 1e-9, so t3 is a constant.

[shiv gaur]

k0=(2*pi/0.6328)*1e6;

t2=1.5e-6;

n1=1.512;n2=1.521;n3=4.1-%i*0.211;

n4=1;

m=0;

x=1;

t3=linspace(1e-9,1e-6,20);

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 = 0;

while (n<=20)

x_new =-(k2).*t2+atan(k1./%i*k2)+atan((k3./k2).*tan(atan(k4./%i*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

plot(t3,x_new)

this is the program pl plot the graph

[Walter Roberson]

What do the % mean in your formula for x_new?

[shiv gaur]

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

Answer 1

[Jan]

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.

[shiv gaur]

k0=(2*pi/0.6328)*1e6;

t2=1.5e-6;

n1=1.512;n2=1.521;n3=4.1-%i*0.211;

n4=1;

m=0;

x=1;

t3=linspace(1e-9,1e-6,20);

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 = 0;

while (n<=20)

x_new =-(k2).*t2+atan(k1./%i*k2)+atan((k3./k2).*tan(atan(k4./%i*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

plot(t3,x_new)

this is the program pl plot the graph

[shiv gaur]

why this is not converging where x is the root of function x_new