A ray of light falls on a prism \(ABC\) \((AB= BC)\) and travels as shown in figure. The refractive index of the prism material should be greater than:

The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is \(30^{\circ}\). One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is: