The angle of incidence

Question

BlackTom AI · Accepted Answer

Snell's law: n1 sin θ1 = n2 sin θ2, so the relationship between incidence and refraction depends on the refractive indices. 1. Relevant knowledge points and concepts - Snell’s law relates the angle of incidence θ1 (measured from the normal) and the angle of refraction θ2 by n1 sin θ1 = n2 sin θ2, where n1 and n2 are the refractive indices of the first and second medium. - The sine function is monotonic increasing for angles between 0° and 90°, so comparisons of sines translate into comparisons of angles in that range. - If n1 = n2, rays travel undeviated (θ1 = θ2). If n1 < n2, rays bend toward the normal (θ2 < θ1). If n1 > n2, rays bend away from the normal (θ2 > θ1). If n1 > n2 and θ1 exceeds the critical angle, total internal reflection occurs (no refracted ray). 2. Step-by-step reasoning - Start with Snell’s law: n1 sin θ1 = n2 sin θ2. - Solve for sin θ2: sin θ2 = (n1/n2) sin θ1. - Compare n1 and n2: - Case A: n1 = n2 → sin θ2 = sin θ1 → θ2 = θ1. - Case B: n1 < n2 → (n1/n2) < 1 so sin θ2 < sin θ1 → θ2 < θ1 (ray refracts toward the normal). - Case C: n1 > n2 → (n1/n2) > 1 so sin θ2 > sin θ1 (for allowed values) → θ2 > θ1 (ray refracts away from the normal). If sin θ2 computed > 1, no refraction (total internal reflection). 3. Intermediate calculation examples - Example 1 (air to glass): n1 = 1.00, n2 = 1.50, θ1 = 30°. sin θ2 = (1.00/1.50)·sin30° = (0.6667)(0.5) = 0.3333 → θ2 ≈ 19.5° (θ2 < θ1). - Example 2 (glass to air): n1 = 1.50, n2 = 1.00, θ1 = 20°. sin θ2 = 1.50·sin20° = 1.50·0.342 = 0.513 → θ2 ≈ 30.9° (θ2 > θ1). 4. Why the correct answer is correct Because Snell’s law shows the ratio n1/n2 dictates whether sin θ2 is smaller, equal, or larger than sin θ1, the angle of incidence may be less than, equal to, or greater than the angle of refraction depending on the media. 5. Why the other options are incorrect - “must equal the angle of refraction.” Wrong: only true when n1 = n2. - “is always less than the angle of refraction.” Wrong: false when n1 < n2 (then θ1 > θ2) or equal when n1 = n2. - “is always greater than the angle of refraction.” Wrong: false when n1 > n2 (then θ1 < θ2) or equal when n1 = n2. 6. Conclusion Therefore the angle of incidence may be greater than, less than, or equal to the angle of refraction, which matches the provided answer: "may be greater than, less than, or equal to the angle of refraction."

The angle of incidence单项选择题

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