You have two containers half full with liquid $1.$ You then fill the two containers respectively with a layer of liquid $2$ and $3.$ A ray of light traveling through the bottom layer $($liquid $1)$ and into the top layer experiences total internal reflection off liquid $2$ when the angle of incidence exceeds $46\mathrm{.}5$ and for liquid $3$ total internal reflection occurs for angles of incidence greater than $50\mathrm{.}7.$ Determine the ratio of the refractive indices of liquids $2$ and $3($n$2/$n$3).$

n$2$n$3$

$=$