For total internal reflection, sini $\gt$ sinC

where, i = angle of incidence, C = critical angle

But, sinC = ${1 \over \mu }$

$\therefore$ sini $\gt$ ${1 \over \mu }$

$\Rightarrow$ $\mu$ $\gt$ ${1 \over {\sin i}}$

$\therefore$ $\mu$ $\gt$ ${1 \over {\sin 45^\circ }}$

$\Rightarrow$ $\mu$ $\gt$ $\sqrt 2$