A cylindrical tube filled with water $\left({\mu }_{\mathrm{w}}=\frac{4}{3}\right)$ is closed at its both ends by two thin, silvered plano-convex lenses, as shown in the figure. Refractive index of lenses $L_1$ and $L_2$ are $2.0$ and $1.5$, while their radii of curvatures are $5\mathrm{ cm}$ and $9 \mathrm{c}\mathrm{m}$, respectively. A point object is placed somewhere at a point $\mathrm{O}$ on the axis of the cylindrical tube. If it is found that all the images formed by multiple refractions and reflections coincide with the object, then the distance between both the lenses is