You are experimentally determining the critical angle for a novel transparent solid whose index of refraction is less than that of water $(n=1\mathrm{.}33)$ but greater than that of air $(n=1\mathrm{.}00).$ Your experimental method involves underwater work in which you observe whether there is any transmitted ray at the water$/$solid interface as you vary the angle of incidence on the solid surface. When your device reaches an incident angle of $53$ degrees you find that the transmitted ray inside the solid vanishes. What is the index of refraction for this new solid?

Multiple Choice

$116$

$0\mathrm{.}57$

$1\mathrm{.}06$

$0\mathrm{.}53$