A ray of light is incident on a prism at an angle of $\displaystyle 45$° and passes symmetrically as shown in the figure. Calculate:

(a)

the angle of minimum deviation,

(b)

the refractive index of the material of the prism, and

(c)

the angle of refraction at the point P.

$$\begin{aligned} & \text { As } \boldsymbol{\delta}=\boldsymbol{\delta}_{\boldsymbol{m}} & \mathrm{r}_{$\displaystyle 1$}=\mathrm{r}_{$\displaystyle 2$} \text { (Altern } & \text { Hence, } \mathrm{r}_{$\displaystyle 1$} \text { (Angle o } & $\displaystyle 1$ \times \sin $\displaystyle 45$=\mu \operatorname{sinr}_{$\displaystyle 1$} & $\displaystyle 1$ \times \frac{1}{\sqrt{2}}=\sqrt{2} \mathrm{sin}_{$\displaystyle 1$} & \therefore \angle r_{$\displaystyle 1$}=$\displaystyle 30$^{\circ} \end{aligned}