Question

What is a necessary condition for total internal reflection
in a medium?

Answer 1

that light ray is incident on the boundary making an angle greater than the critical angle of incidence.
The critical angle of incidence can be found as such :
\[\mu1*\sin i = \mu2 * \sin 90\]

Answer 2

Also that the light ray must be passing from a denser to less dense medium. If the ray is in water going to air it can be totally reflected. But if its going from air to water TIR is impossible.