Wrong Snell's Law

The previous post "Not Snell's Law" dated 03 Jan 2018 is wrong.



Notice the swap $\lambda_i\leftrightarrow a$.

$\cfrac{a*sin(\theta_i)+\lambda_i}{cos(\theta_i)}=OC=\cfrac{\lambda_r}{tan(\cfrac{1}{2}\theta_r)}$

$\cfrac{\lambda_i}{\lambda_r}\cfrac{\cfrac{a}{\lambda_i}*sin(\theta_i)+1}{cos(\theta_i)}=\cfrac{1}{tan(\cfrac{1}{2}\theta_r)}$

If $\cfrac{a}{\lambda_i}\approx 1$ ie a torus with a small hole,

$\cfrac{\lambda_i}{\lambda_r}\cfrac{sin(\theta_i)+1}{cos(\theta_i)}=\cfrac{1}{tan(\cfrac{1}{2}\theta_r)}$

which is the same as before. Wrong!