The X-Y plane be taken as the boundary between two transparent media M_1 and M_2. M_1 in Z ≥ 0 has a refractive index of √ 2 and M_2 with Z <0 has a…

The X-Y plane be taken as the boundary between two transparent media $\displaystyle \mathrm{M}_1$ and $\displaystyle \mathrm{M}_2 . \mathrm{M}_1$ in $\displaystyle \mathrm{Z} \geqslant 0$ has a refractive index of $\displaystyle \sqrt{2}$ and $\displaystyle \mathrm{M}_2$ with $\displaystyle \mathrm{Z}<0$ has a refractive index of $\displaystyle \sqrt{3}$. A ray of light travelling in $\displaystyle \mathrm{M}_1$ along the direction given by the vector $\displaystyle \overrightarrow{\mathrm{P}}=4 \sqrt{3} \hat{i}-3 \sqrt{3} \hat{j}-5 \hat{k}$, is incident on the plane of separation. The value of difference between the angle of incident in $\displaystyle \mathrm{M}_1$ and the angle of refraction in $\displaystyle \mathrm{M}_2$ will be \_\_\_\_ degree.