How to solve for 4 variables from 5 equations that I have derived.

Hi, I have a problem in MATLAB. I am doing research in Optics ... I have to find 4 values from 5 equations and having some trouble. Kindly help.

I have tried reg this as below: I would be grateful to have any suggestions. Thanks in advance

clear

T = 0.89; R = 0.11; lamda = 0.98; d = 1.65; pi = 3.14; phit = 0.6; phir = 0.31; %((-(a))*d) == (23.03)*k;

% sym a b n k; % a and b are "alpha" and "beta"

a = sym('a'); b = sym('b'); n = sym('n'); k = sym('k');

eq1 = T == '({(1-R)^2+4*R*(sin(phir))^2}*exp((-a)*d))/((1-R*exp((-a)*d))^2+4*R*exp((-a)*d)*(sin(b+phir))^2)';

eq2 = (phit) == '((2*(pi)*n*d)/lamda)-(atan((k(n^2+k^2-1))/((k^2+n^2)*(2+n)*n)))+(atan((R*exp((-a)*d))*(sin2(b+phir))/(1-R*exp((-a)*d)*cos2(b+phir))))';

eq3 = (phir) == 'atan(((-2)*k)/(1-((n)^2)-((k)^2)))';

eq4 = (b) == '((2*(pi)*n*d)/lamda)';

eq5 = (a) == '((4*(pi)*k)/lamda)';

%eq6 = (e) == '((-(a))*d) == (23.03)*k';

[a b n k] = solve(eq1,eq2,eq3,eq4,eq5,a,b,n,k);

Answer 1

[Azzi Abdelmalek]

Corrected code

syms a b n k;
eq1 ='T==(((1-R)^2+4*R*(sin(phir))^2)*exp((-a)*d))/((1-R*exp((-a)*d))^2+4*R*exp((-a)*d)*(sin(b+phir))^2)';
eq2 = 'phit==((2*(pi)*n*d)/lamda)-(atan((k(n^2+k^2-1))/((k^2+n^2)*(2+n)*n)))+(atan((R*exp((-a)*d))*(sin2(b+phir))/(1-R*exp((-a)*d)*cos2(b+phir))))';
eq3 = 'phir==atan(((-2)*k)/(1-((n)^2)-((k)^2)))';
eq4 = 'b==((2*(pi)*n*d)/lamda)';
eq5 =  'a==((4*(pi)*k)/lamda)';
sol= solve(eq1,eq2,eq3,eq4,eq5,a,b,n,k)

but it seems that you system does'nt have solutions. Notice that you have more equations then unknown variables

Answer 2

[Shaumik]

Thanks a lot for your help Azzi.. I will work on this and get back.

Answer 3

[Shaumik]

hello

I just put in the value of 'a' in the equations (program given below the error message), but getting this error. Any suggestions would be very helpful. Thanks

________________________________________

??? Error using ==> solve>getEqns at 182 ' T==((1-R)^2)+((4)*(R)*(sin(phir)^2))*(exp((-((4*(pi)*k)/(lamda)))*(d)))/((1)-(R)*(exp(((4*(pi)*k)/(lamda))*(d)))^2)+((4)*(R)*(exp(((4*(pi)*k)/(lamda))*(d)))*(sin(b+phir)^2)) ' is not a valid expression or equation.

Error in ==> solve at 67 [eqns,vars] = getEqns(varargin{:});

Error in ==> RI at 19 sol = solve(eq1,eq2,eq3,eq4,b,n,k);

________________________________________________________

T = 0.89; R = 0.11; lamda = 0.98; d = 1.65; pi = 3.14; phit = 0.60; phir = 0.31;

syms b n k;

eq1 = 'phir==atan(((-2)*k)/(1-((n)^2)-((k)^2)))';

eq2 = 'T==((1-R)^2)+((4)*(R)*(sin(phir)^2))*(exp((-((4*(pi)*k)/(lamda)))*(d)))/((1)-(R)*(exp(((4*(pi)*k)/(lamda))*(d)))^2)+((4)*(R)*(exp(((4*(pi)*k)/(lamda))*(d)))*(sin(b+phir)^2))';

eq3 = 'phit==((2*(pi)*n*d)/(lamda))-(atan((k(n^2+k^2-1))/((k^2+n^2)*(2+n)*n)))+(atan((R*exp(((4*(pi)*k)/(lamda))*d))*(sin2(b+phir))/(1-R*exp(((4*(pi)*k)/(lamda))*d)*cos2(b+phir))))';

eq4 = 'b==(((2)*(pi)*(n)*(d))/(lamda))';

%eq5 = 'a==((4*(pi)*k)/(lamda))';

sol = solve(eq1,eq2,eq3,eq4,b,n,k);

[Walter Roberson]

Change the == to =

[Shaumik]

Thanks Walter.

I changed the equal sign and it gave the following error:

Warning: Explicit solution could not be found.

So, do I have to try with fsolve or are there any other means to solve these equations.

Thanks for the help

[Walter Roberson]

What are sin2() and cos2() ? If you want sin-squared you need sin(x)^2

[Shaumik]

yes, you are right. i may have made a mistake there.

I am correcting that and trying again.

thanks for the help.

Answer 4

[Shaumik]

sorry to bother again.. I changed the sin-square and cos-square, but still the same error is coming. Dont know where I am going wrong.

Anyway.. I am keeping on trying.. meanwhile if you think of anything else that might help, please let me know. Would really appreciate it.

Thanks Walter for all the help.