Split Cannot Mend

Consider this,

$\cfrac{\mu_2}{\mu_1}=\cfrac{tan(\theta_2-\alpha_{2s})}{tan(\theta_1-\alpha)}=\cfrac{tan(\theta_2+\alpha_{2p})}{tan(\theta_1+\alpha)}$

$tan(\theta_2-\alpha_{2s})=\cfrac{\mu_2}{\mu_1}tan(\theta_1-\alpha)$

from which we may obtain $\alpha_{2s}$.  And

$tan(\theta_2+\alpha_{2p})=\cfrac{\mu_2}{\mu_1}tan(\theta_1+\alpha)$

from which we may obtain $\alpha_{2p}$.

And $\theta_2$ is given by,

$\cfrac{ tan(\theta_1)}{tan(\theta_2)}=\cfrac{\varepsilon_2}{\varepsilon_1}$

from the post "A Bloom Crosses Over" dated 10 Aug 2015.

The graph illustrates how to obtain $\alpha_{2s}$ and $\alpha_{2p}$.