Answer
a) $n_2=1.41$
b) $n_2=1.88$
Work Step by Step
a) $n_2=\frac{\sin(\alpha)}{\sin(\beta)}$
$n_2\sin(\gamma)=n_1\sin(\theta)$
$n_2=\frac{1}{\sin(\gamma_{min})}$
$90^o=\beta+\gamma_{min}$
$n_2=\frac{\sin(\alpha_{max})}{\sin(90^o-\gamma_{min})}=\frac{1}{\sin(\gamma_{min})}$
$\cos(\gamma_{min})=\sin(\gamma_{min})$
$\gamma_{min}=45^o$
$n_2=\frac{1}{\sin(\gamma_{min})}=\frac{2}{\sqrt{2}}=1.41$
b) $n_2=\frac{1.33}{\sin(\gamma_{min})}=1.88$
