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