Explanation:
Refractive index of medium,
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mu = \frac{1}{{\sin C}}\)
where, \(C\) is critical angle.
Given, \(\,\,\,\,\,\,\,\,\,C = {30^ \circ }\)
\(\therefore {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \therefore \,\,\,\,\,\,\,\,\,\,\,\mu = \frac{1}{{\sin {{30}^ \circ }}} = \frac{1}{{1/2}} = 2\)
From Snell's law, \(\,\mu = \frac{{{v_0}}}{{{v_m}}}\)
where, \(v_{0}\) is speed of light in vacuum and
\(v_{m}\) the velocity in medium.
\(\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{v_m} = \frac{{3 \times {{10}^8}}}{2} = 1.5 \times {10^8}\;m/s\)