Solution:

Given,

Polarizing Angle, \(\theta_p=60^\circ\) ,
Velocity of light (v) = ?

We have,

\(\mu=\tan\left(\theta\right)\)
Or, \(\mu=\tan\left(60^\circ\right)\)
∴ \(\mu=\sqrt3\)

Again, 

\(\mu=\frac cv\)
Or, \(v=\frac c\mu\)
Or, \(v=\frac{3\times10^8}{\sqrt3}\)
∴ \(v=1.73\times10^8\) m/s

Hence the required velocity of the light in a given medium is 1.73×10^8 m/s.