Warning: Cannot solve symbolically. Returning a numeric approximation instead.

Hello!

I'm trying to use the solve() function to solve a complex equation, but I can't seem to get it right. I keep getting "Warning: Cannot find explicit solution. ". This is my code:

    d2=140; 
    d3=1200;

    n3=1.445; 
    syms n2
    ns=3.5;
    lambda=600;
    k2=n2.*2*pi/lambda;
    k3=n3*2*pi/lambda;

    delta2 = k2*d2;
    delta3 = k3*d3;

    M3 = [cos(delta3) (1i)*sin(delta3)/n3;(1i)*n3*sin(delta3) cos(delta3)];
    M2 = [cos(delta2) (1i)*sin(delta2)/n2;(1i)*n2*sin(delta2) cos(delta2)];

    M=M2*M3;
    sub_vector = [1;ns];
    sol=M*sub_vector; 
    r=(sol(1)-sol(2))/(sol(1)+sol(2));

    solv = solve((abs(r))^2 == 1000,n2)

Answer 1

[Walter Roberson]

You are rarely going to get a closed form solution to a trig function, especially one involving floating point values.

My tests suggest that n2 would have to be imaginary for the expression to equal 1000. Are you expecting an imaginary value? (I have not determined yet whether there are any solutions.)

[Walter Roberson]

My tests show that there are an infinite number of solutions near n2 = complex(1.015,1.217)

[AdamI120]

Thanks for your reply. As you can see, I am calculating the absolute expression of r^2, therefore there is suppose to be no complex values in that expression. n2 is some refractive index, that changes according to the received reflectance R. Any other ideas? For this specific code, if the reflectance is equal to 1000, I'm trying to find n (which should be 2<n2<4).

[Walter Roberson]

No chance. If you plot abs(r)^2 over n2 = 2 to 4 you will find that it is strictly less than 1, and so cannot reach 1000. abs(r)^2 varies a fair bit but the upper limit over the real numbers is +1

In order for abs(r)^2 to reach 1000 then n2 needs to be a complex number whose real part is very close to 1.015 (narrow peak). The imaginary portion has a slightly wider range but not much.