multiply by two matrix

Mj = [cos (kj hj)     i*sin(kj hj) /kj ; i*kj*sin(kj hj)    cos (kj hj) ]; 
kj=sqrt(nj^2*k02-x^2);

Take

n1=1.521;n2=2.66;k0=1;h1=1.5e-6;h2=1e-6

multiply M1*M2

[Image Analyst]

And the question is. . . . 🤔

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

[shiv gaur]

%this is program

function kp1
close all;
clear all;















    function y=F(x)
        
        for t2=1
            k0=1;
            n1=1.521;
            %n2=2.66;
            n2=4.1-0.211*1i;
            
            ns=1.512;
            %nc=0.15-1i*3.2;
            nc=1;
            
            k1=sqrt(n1.^2*k0.^2-x.^2);
            k2=sqrt(n2.^2*k0.^2-x.^2);
            t1=1.5;
            m11= cos(t1*k1)*cos(t2*k2)-(k2/k1)*sin(t1*k1)*sin(t2*k2);
            m12=(1/k2)*(cos(t1*k1)*sin(t2*k2)*1i) +(1/k1)*(cos(t2*k2)*sin(t1*k1)*1i);
            m21= (k1)*cos(t2*k2)*sin(t1*k1)*1i +(k2)*cos(t1*k1)*sin(t2*k2)*1i;
            m22=cos(t1*k1)*cos(t2*k2)-(k1/k2)*sin(t1*k1)*sin(t2*k2);
            
            
            A=[m11 m12 ; m21  m22];
            disp(eig(A))
            
            gs=x.^2-ns.^2*k0.^2;
            gc= x.^2-nc.^2*k0.^2;
            
            y= 1i*(gs*m11+gc*m22)-m21+gc*gs*m12 ;
            
            
            
            
            %y=x^2+x+1;
            
            
            
        end 
    end

p0=1;
p1=1.5;
p2=2;
tol = 10^-5;
n = 50;

h1 = p1 - p0;
h2 = p2 - p1;
del1 = (F(p1)-F(p0))./h1;
del2 = (F(p2)-F(p1))./h2;
d = (del2-del1)./(h2+h1);
I = 3;
%Step 2
while I <= n
    %Step 3
    b = del2+h2.*d;
    D = sqrt(b.^2-4.*F(p2).*d); % could be complex
    %Step 4
    if abs(b - D) < abs(b + D)
        E = b + D;
    else
        E = b - D;
    end
    %Step 5
    h = -2.*F(p2)./E;
    p = p2 + h;
    
    if I == 3
        table{1} = 'Muller''s Method Iterations';
        table{2}='  I             P                     f(P)           ';
        table{3}='-----------------------------------------------------';
    end
    str = sprintf('%3u:  % 6.6f + %6.6fi % 6.6f + %6.6fi',I,real(p),imag(p),real(F(p)),imag(F(p)));
    table{I + 1} = str; %#ok<*AGROW>    
    
    %Step 6
    if abs(h) < tol
        val = p;
        table = char(table);
        
        break
    end
    
    p0 = p1;
    p1 = p2;
    p2 = p;
    h1 = p1 - p0;
    h2 = p2 - p1;
    del1 = (F(p1)-F(p0))./h1;
    del2 = (F(p2)-F(p1))./h2;
    d = (del2-del1)./(h2+h1);
    I = I + 1;
    
end
disp(p)
end

[Jan]

Please format your code properly. Use the icons on top of the field for editing in the forum.

You still did not ask a question.

Answer 1

[Walter Roberson]

syms x
n = [1.521, 2.66];
k0 = 1;
h = [1.5e-6, 1e-6];
k = @(j) sqrt(n(j).^2*k0.^2-x.^2);
M = @(j) [
            cos(k(j) .* h(j)), i*sin(k(j) .* h(j))/k(j)
            i .* k(j) .* sin(k(j).*h(j)), cos(k(j) .* h(j))
            ]

M = function_handle with value:
    @(j)[cos(k(j).*h(j)),i*sin(k(j).*h(j))/k(j);i.*k(j).*sin(k(j).*h(j)),cos(k(j).*h(j))]

M12 = M(1) * M(2)

M12 =