If the angle of incidence is 45 degrees and the angle of refraction is 30 degrees, what is the refractive index of the medium with respect to air?

According to Snell's law of refraction, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given colour of light and a given pair of media.

This constant value is referred to as the refractive index of the second medium with respect to the first. 

$\mathrm{Refractive} \mathrm{index} \left(\mathrm{\mu }\right)= \frac{\sin \mathrm{i}}{\sin \mathrm{r}}$

We have been given, $\angle \mathrm{i}=45°, \angle \mathrm{r}=30°$

$\mathrm{\mu } = \frac{\sin 45°}{\sin 30°}$
$\mathrm{\mu } = \frac{1/\sqrt{2}}{1/2}= \frac{2}{\sqrt{2}}= \sqrt{2}$

Therefore, the refractive index of the medium with respect to air will be $\sqrt{2}$.