(i) Calculation of speed of light
(ii) Calculation of angle of incidence at face AB
(i) $\mathit{\mu }=\frac{\mathit{s}\mathit{i}\mathit{n}\left(\frac{\mathit{A}+{\mathit{\delta }}_{\mathit{m}}}{2}\right)}{\mathit{s}\mathit{i}\mathit{n}\left(\frac{\mathit{A}}{2}\right)}$
$=\frac{\mathit{s}\mathit{i}\mathit{n}\left(\frac{{60}^{\circ }+{30}^{\circ }}{2}\right)}{\mathit{s}\mathit{i}\mathit{n}\left(\frac{{60}^{\circ }}{2}\right)}=\sqrt{2}$

$\mathit{v}=2.122\times {10}^8\mathrm{m}∕\mathrm{}\mathit{s}$
(ii)
At face $\mathrm{AC}$, let the angle of incidence be ${\mathit{r}}_2$.
For grazing ray, $\mathit{e}={90}^{\circ }$
$\Rightarrow \mathit{\mu }=\frac{1}{\mathit{s}\mathit{i}\mathit{n}{\mathit{r}}_2}\Rightarrow {\mathit{r}}_2=\mathit{s}\mathit{i}\mathit{n}{}^{-1}\left(\frac{1}{\sqrt{2}}\right)={45}^{\circ }$
Let angle of refraction at face $\mathrm{AB}$ be ${\mathit{r}}_1$.
Now ${\mathit{r}}_1+{\mathit{r}}_2=\mathit{A}$
$\therefore {\mathit{r}}_1=\mathrm{A}-{\mathit{r}}_2={60}^{\circ }-{45}^{\circ }={15}^{\circ }$
Let angle of incidence at this face be $\mathit{i}$
$\mathit{\mu }=\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{i}}{\mathit{s}\mathit{i}\mathit{n}{\mathit{r}}_1}$
$\Rightarrow \mathit{\mu }=\sqrt{2}=\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{i}}{\mathit{s}\mathit{i}\mathit{n}{15}^{\circ }}$
$\therefore \mathit{i}=\mathit{s}\mathit{i}\mathit{n}{}^{-1}\left(\sqrt{2}\cdot \mathit{s}\mathit{i}\mathit{n}{15}^{\circ }\right)$