a
(a) From figure it is clear that \(TIR\) takes place at surface \(AC\) and \(BC\)

i.e. \({45^o} > C\)

\( \Rightarrow \sin {45^o} > \sin C\)

\( \Rightarrow \frac{1}{{\sqrt 2 }} > \frac{1}{\mu }\)

\( \Rightarrow \mu > \sqrt 2 \)

Hence \({\mu _{least}} = \sqrt 2 \)