c
Refractive index for medium \(M_{1}\) is

\({\mu _1} = \frac{c}{{{v_1}}} = \) \(\frac{{3 \times {{10}^8}}}{{1.5 \times {{10}^8}}} = 2\)

Refractive index for medium \(M_{2}\) is

\({\mu _2} = \frac{c}{{{v_2}}} = \) \(\frac{{3 \times {{10}^8}}}{{2.0 \times {{10}^8}}} = \frac{3}{2}\)

For total internal reflection, \(\sin i \geq \sin C\)

where \(i=\) angle of incidence, \(C=\) critical angle But \(\sin C=\frac{\mu_{2}}{\mu_{1}}\)

\(\sin i \geqslant \frac{{{\mu _2}}}{{{\mu _1}}} \geqslant \) \(\frac{{3/2}}{2} \Rightarrow \) \(i \geqslant {\sin ^{ - 1}}\left( {\frac{3}{4}} \right)\)