Brewster's Angle & Malus' Law: The Physical Optics of Polarized Glare Extinction on Water & Asphalt

When light strikes an interface between two transparent media with refractive indices $n_1$ and $n_2$, reflected light becomes completely linearly S-polarized (horizontal) at Brewster's Angle ($\theta_B$), where reflected and refracted rays are perpendicular ($90^\circ$):

$$\tan \theta_B = \frac{n_2}{n_1} \implies \begin{cases} \mathbf{\text{Water } (n_2 = 1.333):} & \theta_B = \tan^{-1}(1.333) = \mathbf{53.1^\circ} \\ \mathbf{\text{Glass/Asphalt } (n_2 = 1.52):} & \theta_B = \tan^{-1}(1.52) = \mathbf{56.7^\circ} \end{cases}$$

At angles near $53^\circ\text{--}57^\circ$ (typical sun angles during driving and maritime activities), reflected glare is virtually $100\%$ horizontally polarized.

According to Malus' Law, the transmitted luminous intensity $I$ of linearly polarized light passing through a polarizer with transmission axis oriented at angle $\theta$ is:

$$I = I_0 \cdot \cos^2\theta \implies \text{When } \theta = 90^\circ \ (\text{Horizontal Glare vs Vertical Lens Axis}) \implies \mathbf{I = 0}$$

Because polarized sunglasses orient their transmission axis strictly vertically ($90^\circ$ to horizontal glare), blinding roadway and water surface glare is attenuated by over $99.0\%$ to $99.9\%$, while ambient vertical light passes freely.

Ophthalmic polarizing quality is graded by the Polarization Efficiency ($PE$):

$$PE = \sqrt{\frac{T_{\text{parallel}} - T_{\text{crossed}}}{T_{\text{parallel}} + T_{\text{crossed}}}} \times 100\% \implies \mathbf{\text{ELLASUV Benchmark: } PE > 99.5\%}$$

Low-quality sunglasses achieve only $70\text{--}80\%\ PE$, leaving noticeable wash-out glare across wet highways.