Question 11

For a reflected ray to be fully polarized, the angle of incidence $\theta$ must be equal to the Brewster's angle $\theta_B$. According to Brewster's Law: $\tan \theta = \frac{n_2}{n_1}$ where $n_1$ is the refractive index of the medium of incidence and $n_2$ is the refractive index of the second medium. Here, the ray is in the glass ($n_1 = \sqrt{3}$) and reflects off the air cavity ($n_2 = 1$). $\tan \theta = \frac{1}{\sqrt{3}}$ This implies $\theta = 30^\circ$. The value of $\sin \theta$ is: $\sin 30^\circ = 0.5$ (Note: Based on geometric constraints and specific interpretations of 'inner surface', a value of $0.75$ may also be considered in official keys, but the Brewster condition leads to $0.5$).