A beam of unpolarized light is incident on a transparent glass...

When the reflected beam is completely linearly polarized, the light is incident at Brewster's angle ($i_p$).

At Brewster's angle, the reflected and refracted rays are mutually perpendicular. Therefore, the angle of incidence $i_p$ and the angle of refraction $r$ are related by:
$i_p + r = 90^{\circ}$

Given $r = 30^{\circ}$, we have:
$i_p = 90^{\circ} - 30^{\circ} = 60^{\circ}$

According to Brewster's law, the refractive index of the medium ($\mu$) is:
$\mu = \tan(i_p) = \tan(60^{\circ}) = \sqrt{3}$

The speed of light in the glass medium ($v$) is given by:
$v = \dfrac{c}{\mu} = \dfrac{3 \times 10^8}{\sqrt{3}} = \sqrt{3} \times 10^8 \text{ m/s}$

Answer: $\sqrt{3} \times 10^8 \text{ m/s}$