A point object $O$ is placed on the axis of a cylindrical piece of glass of refractive index $1.6$ as shown in the figure. One surface of the glass piece is convex with radius of curvature $3\;\text{mm}$. The point appeared to be at $5\;\text{mm}$ on the axis when viewed along the axis and from the right side of the convex surface. The distance of the point object from the convex surface is