After doing experiment with Michelson interferometer I need to calculate two coefficients: k and n. This involves solving two equations for k and n:
$$\frac{(8 \pi d)}{\lambda }{kn}=\frac{\text{$\triangle $I}}{I}$$
$$\text{$\triangle $l}_2=\left\{\frac{\lambda }{2 \pi }\right\} \tan ^{-1}\left(\frac{2 \left(n \sin \left(\frac{4 \pi d n}{\lambda }\right)+k\right)}{\frac{4 \pi d \left(n^2-1\right)}{\lambda }+\left(n^2+1\right) \cos \left(\frac{4 \pi d n}{\lambda }\right)}\right)$$
For the first one I have everything exept $\Delta$*r*. As for second one, I have all coefficients. But Mathematica won't solve it neither with Solve, neither with NSolve.
Solve[{k*n==0.00730621,
1.67/0.00539535==ArcTan[(2(k+n Sin[8.89655n]))/(8.89655(-1+n^2)+(1+n^2)Cos[8.89655 n])]},
{k,n}]
It just goes into ever increasing evaluation till computer starts to freeze or I stop evaluation.
Could anyone suggest how I tackle this problem? Thanks.
n
, plugging that into the second equation, then plotting that equation as a function ofn
and seeing roughly where the roots are. Then useFindRoot
. $\endgroup$k
in terms ofn
and plug the result into the second equation. ThenPlot[ f[n] , {n,-10,10}]
to see that there is no zero. This suggests that there is something strange with the parameter numbers calculated before. $\endgroup$