The figure shows the path of a ray passing through an equiangular prism $PQR$. It is incident on face $PR$ at an angle slightly greater than the critical angle for total internal reflection. If the angle $\alpha$ shown in the figure is $30°$. Calculate the Refractive index of the material of the prism.

In the figure shown $S$ is a monochromatic point source emitting light of wavelength $=500 \mathrm{nm}$. A thin lens of circular shape and focal length $0.10 \mathrm{m}$ is cut into two identical halves $L_1$ and $L_2$ by a plane passing through a diameter. The two halves are placed symmetrically about the central axis SO with a gap of $0.5 \mathrm{mm}$. The distance along the axis from $S$ to $L_1$ and $L_2$is $0.15 \mathrm{m}$, while that from $L_1$ and $L_2$ to $O$ is $1.30 \mathrm{m}$.

The screen at $O$ is normal to SO. (i) If the third intensity maximum occurs at the point $A$ on the screen, find the distance OA. (ii) If the gap between $L_1$ and $L_2$ is reduced from its original value of $0.5 \mathrm{mm}$, will the distance OA increase decrease or remain the same?