A beam of unpolarized light is incident on a glass surface at...

According to Brewster's Law, light reflected at Brewster's angle is completely plane-polarized. Let the intensity of this reflected light be I_\max.

Initially, the transmitted intensity is zero, which means the pass axis of the polaroid is perpendicular to the plane of polarization of the reflected light (angle is $90^{\circ}$).

When the polaroid is rotated by an angle $\theta$ from this initial position, the angle between its pass axis and the plane of polarization becomes $(90^{\circ} - \theta)$.

By Malus's Law, the transmitted intensity $I_t$ is:
I_t = I_\max \cos^2(90^{\circ} - \theta) = I_\max \sin^2\theta

The intensity blocked by the polaroid $I_b$ is the remaining portion of the incident light:
I_b = I_\max - I_t = I_\max (1 - \sin^2\theta) = I_\max \cos^2\theta

We are given that the transmitted intensity is one-third of the blocked intensity:
$I_t = \dfrac{1}{3} I_b$

Substituting the expressions for $I_t$ and $I_b$:
I_\max \sin^2\theta = \dfrac{1}{3} I_\max \cos^2\theta

$\dfrac{\sin^2\theta}{\cos^2\theta} = \dfrac{1}{3}$

$\tan^2\theta = \dfrac{1}{3}$

$\tan\theta = \dfrac{1}{\sqrt{3}}$

Therefore, $\theta = 30^{\circ}$.

Answer: $30^{\circ}$