Solving for an mathematical expression under certain parametric conditions

Hello,

How do I solve a mathematical expression for certain conditions?

For example, how do I solve for A or FIE in the limit x<<eps2?

Please, find attached my code.

syms n0 ns eps2 x
% ne=n0*Sin[theta0];
% n0=1;
% ns=1.5;
neu=ns*n0^(-1);
thetac=asind(neu);%critical angle
thetab=atand(neu);%Brewster's angle
thetaqb=acosd(((neu^2-1)*sqrt(neu^2+1))*(neu^4+1)^(-1));%Pseudo-Brewster angle
theta0=thetaqb;%The critical angle of 41.8 degrees,...
%the quasi-Brewster angle of 69.2 degrees,...
%and the pseudo-Brewster angle of 84.8 degrees.
ne=n0*sind(theta0);
% thetas=ArcSin[ne/ns];
thetas=asind(ne*ns^(-1));
% Z0=n0/Cos[theta0];
Z0=n0*cosd(theta0)^(-1);
% Zs=ns/Cos[thetas];
Zs=ns*cosd(thetas);
% n2=ne^2-I*eps2;
% eps2=;
n2=ne^2-1i*eps2;
% m11=1+(n2*(x^2))/2;
% x=;
m11=1+(n2*x^2)*0.5;
% m12=x*n2/eps2;
m12=x*n2*eps2^(-1);
% m21=x*eps2;
m21=x*eps2;
% m22=m11;
m22=m11;
% dnm=(m11+m12*Zs)*Z0+(m21+m22*Zs);
dnm=(m11+m12*Zs)*Z0+(m21+m22*Zs);
% r=((m11+m12*Zs)*Z0-(m21+m22*Zs))/dnm;
r=((m11+m12*Zs)*Z0-(m21+m22*Zs))*dnm^(-1);
% t=2*Z0/dnm;
t=2*Z0*dnm^(-1);
% R=Abs[r]^2;
R=abs(r)^2;
% T=Re[Zs]/Z0*(Abs[t]^2);
T=real(Zs)*(Z0*abs(t)^2)^(-1);
% A=1-T-R;
A=1-(T+R);
% FIE=n0*A*Cos[theta0]/eps2/x;
FIE=(n0*A*cosd(theta0))*(eps2*x)^(-1);

Answer 1

[Guru Mohanty]

Hi, I understand you want to solve a equation under some parametric condition. To set some parametric condition you can use assume function. Here is a sample code using assume function.

syms x y 
assume(x>y)
expr1 = 2*x-3*y==0;
expr2 = x + y ==2;
expr = [expr1;expr2];
solve(expr)

[Walter Roberson]

Note: solve() does not always pay attention to assumptions. When you get a result from solve() it is always a good idea to check that it really does pass all of the requirements.