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Reflection and refraction at boundaries (Fresnel equations, introductory)

Maxwell's equations · Physics

Study notes

Light in air (n₁ = 1.00) hits glass (n₂ = 1.50). (a) Find the reflectance at normal incidence. (b) Find Brewster's angle. (c) At Brewster's angle, what is the polarisation of the reflected ray? Step 1: Normal incidence: amplitude r = (n₁ − n₂)/(n₁ + n₂) = (1 − 1.5)/2.5 = −0.2. Reflectance R = r² = 0.04 = 4% per surface. (The minus sign is a 180° phase flip of the reflected wave.) Step 2: tanθ_B = n₂/n₁ = 1.50 → θ_B = arctan(1.5) ≈ 56.3° from the normal. Step 3: At θ_B, r_p = 0 — the parallel-polarised component is entirely transmitted, none reflected. The reflected ray is 100% s-polarised (perpendicular to the plane of incidence). Photographers use a polarising filter at this geometry to kill reflections off water/glass completely.

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