A cylindrical vessel, whose diameter and height both are equal to $30 cm,$ is placed on a horizontal surface and a small particle $P$ is placed in it at a distance of $5.0 cm$ from the centre. An eye is placed at a position such that the edge of the bottom is just visible. The particle $P$ is in the plane of the drawing. The minimum height (in $cm$) upto which water should be poured in the vessel to make the particle $P$ visible is ____ . (Refractive index of water $=\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$)