Optical Fibre Communication?
In an optical fibre communication system, the light signal transmitted through a fibre is diminished due to the total internal reflection. If the angle of incidence exceeds the critical angle, the signal gets lost. Considering the refractive indices of fibre and surrounding medium as μ and μ₀ respectively, derive an expression for the maximum angle of incidence for the signal to be transmitted effectively using the arccosine function.
1 Answer
📌 CONCEPT: In an optical fibre communication system, the maximum angle of incidence for signal transmission is determined by the critical angle, beyond which total internal reflection occurs.
📐 RULE / FORMULA: The critical angle θc is given by the formula sin(θc) = μ₀ / μ, where μ and μ₀ are the refractive indices of the fibre and surrounding medium respectively.
💡 WORKED EXAMPLE: Suppose the refractive index of the fibre μ = 1.5 and that of the surrounding medium μ₀ = 1.0. Using the formula sin(θc) = μ₀ / μ, we can calculate the critical angle as θc = arcsin(1/1.5) = arcsin(0.6667) ≈ 41.81°.
⚠️ COMMON MISTAKE: Students often confuse the refractive indices of the fibre and surrounding medium, or incorrectly apply the formula to calculate the critical angle, leading to incorrect results.
10 Aug 26
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