Cross-section view of a prism is the equilateral triangle $A B C$ in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from $P$ (midpoint of $B C$ ) to $A$ is $\_\_\_\_$ $\times 10^{-10} \mathrm{~s}$.
(Given, speed of light in vacuum $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ and $\cos 30^{\circ}=\frac{\sqrt{3}}{2}$ )