For a given angle of incidence and a prism arrangement shown in the figure, the minimum refractive index for total internal reflection is:
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For a given angle of incidence and a prism arrangement shown in the figure, the minimum refractive index for total internal reflection is:

G1 Physics · Accepted Answer

Step 1: Refraction at first surface: sin45° = μ sin r. Step 2: At second face, threshold of TIR is C = 90° − r, with sin C = 1/μ, so cos r = 1/μ. Step 3: Thus sin r = 1/(√2 μ). Apply sin²r + cos²r = 1: 1/(2μ²) + 1/μ² = 1. Step 4: μ² = 3/2 ⇒ μ = √(3/2). Final answer: (C) √(3/2).