A plane polarized blue light ray is incident on a prism such that...

For no reflection:

$tani = \sqrt{3}$

$⇒ i = 60 °$

Applying Snell's law at left interface, we get

$⇒ 1 \times sini = \sqrt{3} \times sin{r}_{1} ⇒ sin{r}_{1} = \dfrac{1}{2} ⇒ {r}_{1} = {30}^{o}$

Now, for given values

$\delta = i + e - A ⇒ 60 ° = 60 ° + e - A ⇒ e = A$

Then,

$A = {r}_{1} + {r}_{2} ⇒ {r}_{2} = A - {r}_{1} = {30}^{o}$

For red light:

Expression to find minimum deviation is given by,

$\mu = \dfrac{\sin \left(\dfrac{A + {\delta}_{m}}{2}\right)}{\sin \left(\dfrac{A}{2}\right)} = \dfrac{\sin \left(\dfrac{60 ° + 30 °}{2}\right)}{\sin \left(\dfrac{60 °}{2}\right)} = \dfrac{\dfrac{1}{\sqrt{2}}}{\dfrac{1}{2}} = \sqrt{2}$