root finding and plot of graph

function y=f(x,t3)

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;

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);

y=-(k2)*t2+atan(k1/1i*k2)+atan((k3/k2)*tan(atan(k4/1i*k2)-k3*t3))+m*pi;

end

pl plot the graph between t3 vs x(real) ,t3 vs x(imag)

t3=1e-9:1e-6;

pl pl help to plot

Answer 1

[Alan Stevens]

Are you looking for something like this?

hi = 1e-6; lo = 1e-9;
n = 500;
dt = (hi-lo)/n;

t3 = lo:dt:hi;
y = f(t3);
subplot(2,1,1)
plot(t3,real(y)),grid
xlabel('t3'),ylabel('real part of y')
subplot(2,1,2)
plot(t3,imag(y)),grid
xlabel('t3'),ylabel('imaginary part of y')

function  y=f(t3)
 
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;
k1=k0*sqrt(n1^2-t3.^2);
k2=k0*sqrt(n2^2-t3.^2);
k3=k0*sqrt(n3^2-t3.^2);
k4=k0*sqrt(n4^2-t3.^2);
y=-(k2).*t2+atan(k1./1i.*k2)+atan((k3./k2).*tan(atan(k4./1i.*k2)-k3.*t3))+m*pi;
end

[shiv gaur]

no first we have to find the value of x ie transcedental equation then plot between t3,x

Answer 2

[shiv gaur]

function metal4

%T2 = 1e-9:1e-9:1e-6;

%T3=linspace(1e-9,1e-7,35);

T3=1e-9:1e-8:1e-7;

for j=1:numel(T3)

t3 = T3(j);

p0 = 0.5;

p1 = 1;

p2 = 1.5;

TOL = 10^-2;

N0 = 100; format long

h1 = p1 - p0;

h2 = p2 - p1;

DELTA1 = (f(p1,t3) - f(p0,t3))/h1;

DELTA2 = (f(p2,t3) - f(p1,t3))/h2;

d = (DELTA2 - DELTA1)/(h2 + h1);

i=3;

while i <= N0

b = DELTA2 + h2*d;

D = (b^2 - 4*f(p2,t3)*d)^(1/2);

if abs(b-D) < abs(b+D)

E = b + D;

else

E = b - D;

end

h = -2*f(p2,t3)/E;

p = p2 + h;

if abs(h) < TOL

%disp(p)

break

end

p0 = p1;

p1 = p2;

p2 = p;

h1 = p1 - p0;

h2 = p2 - p1;

DELTA1 = (f(p1,t3) - f(p0,t3))/h1;

DELTA2 = (f(p2,t3) - f(p1,t3))/h2;

d = (DELTA2 - DELTA1)/(h2 + h1);

i=i+1;

end

if i > N0

formatSpec = string('The method failed after N0 iterations,N0= %d ');

fprintf(formatSpec,N0);

end

%P(j)=abs(imag(p)*8.57e5);

P(j)=abs(real(p));

end

plot(T3,P)

end

function y=f(x,t3)

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;

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);

y=-(k2)*t2+atan(k1/1i*k2)+atan((k3/k2)*tan(atan(k4/1i*k2)-k3*t3))+m*pi;

end