An observer can see through a pin hole the top end of a thin rod of height h, placed as shown. The beaker height is 3 h and its radius is h. When the beaker is filled with a liquid up to a height 2h ,he can see the lower end of the rod. Then RI of liquid is .

Question

$(a)\;\frac{5}{2} \\ (b)\;\sqrt {\frac{5}{2}} \\ (c)\;\sqrt {\frac{3}{2}} \\ (d)\;\frac{3}{2} $