Error in plotting function of atand against different values of angle

Hi All, I am getting error Error using atand Argument should be real while executing below code. Kindly help to correct it.

n1=1.51;
n2=1;
anglec = asind (n2/n1);
angleTE=[];
angleTM=[];
for angle= 1:20:90
    angleTE(angle)= 2*atand((sqrt (((sind (angle))^2) - ((sind (anglec))^2))) / (cosd (angle)));
    angleTM(angle) = 2*atand( (sqrt (((sind(angle))^2) - ((sind (anglec))^2))) / ((cosd (angle))*(sind(anglec))^2));
end
plot(angle,angleTE)
plot(angle,angleTM)

Answer 1

[Walter Roberson]

When angle < anglec then sind(angle)^2 < sind(anglec)^2 so subtracting the two gives a negative and sqrt() of a negative is imaginary.

Side note: as both expressions have (sqrt (((sind (angle))^2) - ((sind (anglec))^2))) in the numerator, calculate that once per loop iteration and then the two angle calculations simplify.

You should be considering whether you should use atan2() and then converting the radian answer to degrees.

[Muhammad Rehan]

I have very little knowledge of programming and need to implement this equation in MATLAB to plot ıts graph. Can you suggest some necessary changes in code for it to work. Thanks

[Walter Roberson]

Please show the original equations that you need to implement, perhaps as an image of the equation (you can attach jpg images by using the paperclip icon)

[Muhammad Rehan]

I am trying to write these equations in MATLAB and then trying to plot their graph w.r.t theta(i). Thanks

[Walter Roberson]

Is there perhaps something in the phrasing of the question to indicate that theta1 must be greater than thetac ? Because the expression in the sqrt() can definitely end up negative.

[Muhammad Rehan]

yes you are right i have modified the code but now getting error in plot command.

Error using plot Vectors must be the same lengths.

 n1=1.51;
n2=1;
anglec = asind (n2/n1);
angle= 42:1:90;
for ii = 42:1:90
    angleTE(ii)= 2*atand((sqrt (((sind (ii))^2) - ((sind (anglec))^2))) / (cosd (ii)));
    angleTM(ii) = 2*atand( (sqrt (((sind(ii))^2) - ((sind (anglec))^2))) / ((cosd (ii))*(sind(anglec))^2));
end
plot(angle,angleTE)