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Answer: Brewster’s law: the tangent of the polarising angle is equal to the refractive index of the reflecting medium, \(\tan\theta_B = n\).

When unpolarised light is incident on a transparent surface at a particular angle \(\theta_B\) (the polarising or Brewster angle), the reflected light is completely plane polarised (vibrations perpendicular to the plane of incidence). At this angle the reflected and refracted rays are perpendicular to each other.

Derivation: Let light in air be incident at \(\theta_B\) on a medium of refractive index \(n\), and let \(r\) be the angle of refraction. Since the reflected and refracted rays are at \(90^\circ\),

\[\theta_B + 90^\circ + r = 180^\circ \Rightarrow r = 90^\circ - \theta_B\]

By Snell’s law,

\[n = \frac{\sin\theta_B}{\sin r} = \frac{\sin\theta_B}{\sin(90^\circ - \theta_B)} = \frac{\sin\theta_B}{\cos\theta_B}\]\[\therefore \tan\theta_B = n \quad\text{or}\quad \theta_B = \tan^{-1}(n)\]

For glass (\(n = 1.5\)), \(\theta_B \approx 56.3^\circ\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report
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