Physics - Geometrical Optics Question with Solution | TestHub

Two equilateral-triangular prisms ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism $P_1$ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum deviation in prism $P_2$. If the respective refractive indices of ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are $\sqrt{\frac{3}{2}}$ and $\sqrt{3}$, then $\theta ={\sin }^{-1}\left[\sqrt{\frac{3}{2}}\sin \left(\frac{\pi }{\beta }\right)\right]$, where the value of $\beta$ is _______ .