Polarization And Brewster's Law

Brewster's law states that reflected light is completely plane-polarized when the reflected and refracted rays are mutually perpendicular, which happens at the polarizing angle satisfying $\tan {\theta }_B=n$, where $n$ is the refractive index of the second medium relative to the first. For glass with $n=1.5$, ${\theta }_B={\tan }^{-1}(1.5)\approx 56.3°$. At this incidence the electric field of the reflected light vibrates entirely perpendicular to the plane of incidence. The physical reason is that at this geometry the would-be reflected ray is aligned with the dipole oscillation direction of the refracted beam's charges, and an oscillating dipole radiates no energy along its own axis, so the parallel-polarized component vanishes from the reflection. Only the perpendicular component survives, leaving the reflected beam fully plane-polarized while the transmitted beam remains only partially polarized. The value 33.7° is wrong because it is the complementary refraction angle $90°-{\theta }_B$, not the angle of incidence. The value 41.8° is wrong as it is the critical angle for glass, an unrelated total-internal-reflection threshold. The value 45° is wrong since $\tan 45°=1$ would require $n=1$, i.e. no interface. This NCERT law underlies polarizing sunglasses and photographic filters. A consistency check confirms that at Brewster's angle the sum of the polarizing and refraction angles is exactly 90°.