How do I get normal numerical answers using solve or vpasolve?
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I'm currently making a function within which I determine a Reflectivity value by solving the equation using solve().
However, the answers given are always values of pi, how do I solve this?
[Result, y] = lorentz(0, 0.725, 15)
function [Result, y] = lorentz(position, CavityLength, BaseRD)
%Enter position, cavity length in m and baserd in microseconds.
c = 299792458; %speed of light in m/s
BaseRD = BaseRD*10^-6;
syms Reflectivity
S = vpasolve(((pi*sqrt(Reflectivity))/(1-Reflectivity))/(c/(2*CavityLength)) == BaseRD, Reflectivity, [0.99 1]);
Result.Reflectivity = S;
Result.Finesse = (pi*sqrt(Result.Reflectivity)/(1-Result.Reflectivity));
Result.FSR = c/(2*CavityLength);
FWHM = Result.FSR./Result.Finesse;
Result.HWHM = FWHM/2;
x = linspace(-1e3,1e3,1e5);
y = (1/pi).*(Result.HWHM./(((x-position).^2)+Result.HWHM.^2));
%y = y.*(height/max(y));
%plot(x,y)
end
Reflectivity: 0.99898752118560808161741982765188
Finesse: 987.1748605317811539461548191278*pi
FSR: 206753419.310345
HWHM: 104719.75511965978378924223514237/pi
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Dyuman Joshi
2023-11-30
The BaseRD value is different. And you get your answer.
Also, your comment was marked spam by the Auto Filter, idk how. I have removed the spam notice, and subsequently your flag as well.
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John D'Errico
2023-11-30
vpa will turn those products involving pi into more normal looking numbers. For example...
x = 17*sym(pi)
So x has pi in it.
vpa(x)
vpa yields a symbolic high precision floating point number. But double will also work, and create a double as a result.
double(x)
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