Light enters from air into a given medium at an angle of 45 ° with...

Given here, $i = 45 °$

Deviation in light ray, $D = i - r$, here, $r$ is refracted ray.

$⇒ 15 ° = 45 - r ⇒ r = 30 °$

Using Snell's law,

${n}_{1}sini = {n}_{2}sinr$

$⇒ 1\sin 45 ° = \mu sin30 °$

$⇒ \dfrac{1}{\sqrt{2}} = \mu\dfrac{1}{2}$

Thus, the refractive index of the medium is $\mu = \sqrt{2} = 1 . 414$