State Brewster's law and derive it. Find the polarising angle for glass of refractive index 1.5.

1. 1 · State the law. When light falls on a surface at the polarising angle iₚ, the reflected light is completely plane polarised, and μ = tan iₚ.
2. 2 · Draw the diagram. [Surface with a dashed normal; unpolarised incident ray at iₚ; reflected ray (dots only) at iₚ; refracted ray at r; 90° marked between the reflected and refracted rays]
3. 3 · Use the 90° condition. iₚ + 90° + r = 180°, so r = 90° − iₚ.
4. 4 · Apply Snell's law. μ = sin iₚ / sin(90° − iₚ) = sin iₚ / cos iₚ = tan iₚ.
5. 5 · Calculate. For μ = 1.5: iₚ = tan⁻¹ 1.5 ≈ 56.3°.
6. 6 · Real life. Polaroid sunglasses absorb this polarised glare from water and roads.
7. 7 · Close in one line. So, measuring the polarising angle gives the refractive index of a material.

Scoring tip: Mark the 90° between the reflected and refracted rays on the diagram; the whole proof rests on it.