A point source of light $S$ is placed at the bottom of a vessel containing a liquid of refractive index ${\rm{5}}\,{\rm{/}}\,{\rm{3}}$. A person is viewing the source from above the surface. There is an opaque disc $D$ of radius $1\,\,cm$ floating on the surface of the liquid. The centre of the disc lies vertically above the source $S$. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is<br />.