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A light ray enters at point A, and the refracted ray follows the path AB. The angle of incidence at the lateral face is θ. For total internal reflection to occur at the lateral face, θ must satisfy the condition θ > C or sin θ > sin C. Additionally, since θ + r = 90°, it follows that θ = (90° − r). Which statement is correct?

1. A light ray enters at point A, and the refracted ray follows the path AB. The angle of incidence at the lateral face is θ. For total internal reflection to occur at the lateral face, θ > C or sin θ > sin C. Additionally, since θ + r = 90°, it follows that θ = (90° − r).
2. A light ray enters at point A, and the refracted ray follows the path AB. The angle of incidence at the lateral face is θ. For total internal reflection to occur at the lateral face, θ < C or sin θ < sin C. Additionally, since θ + r = 90°, it follows that θ = (90° − r).
3. A light ray enters at point A, and the refracted ray follows the path AB. The angle of incidence at the lateral face is θ. For total internal reflection to occur at the lateral face, θ = C or sin θ = sin C. Additionally, since θ + r = 90°, it follows that θ = (90° − r).
4. A light ray enters at point A, and the refracted ray follows the path AB. The angle of incidence at the lateral face is θ. For total internal reflection to occur at the lateral face, θ ≠ C or sin θ ≠ sin C. Additionally, since θ + r = 90°, it follows that θ = (90° − r).

Correct answer: A light ray enters at point A, and the refracted ray follows the path AB. The angle of incidence at the lateral face is θ. For total internal reflection to occur at the lateral face, θ > C or sin θ > sin C. Additionally, since θ + r = 90°, it follows that θ = (90° − r).

Solution

For no refraction at the lateral face, the angle of incidence θ must be greater than the critical angle C, i.e., θ > C or sin θ > sin C. The relationship θ + r = 90° implies θ = (90° − r). This matches the explanation in option A.

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