What is the critical angle theta_c for total internal reflection at a boundary from a medium of refractive index n into air (n_air = 1)?
Answer and explanation
Correct answer: D. sin(theta_c) = 1 / n
- Step 1: By Snell's Law, n1 sin(theta1) = n2 sin(theta2). At the critical angle, refracted ray travels along boundary (theta2 = 90 deg). Step 2. n sin(theta_c) = 1 sin(90 deg) = 1 => sin(theta_c) = 1 / n. Answer: sin(theta_c) = 1 / n. Why not the others:* cos(theta_c) = 1/n uses cosine; tan(theta_c) = n is Brewster's law for polarization; sin(theta_c) = n would exceed 1 for dense media.
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