Prism — Normal Incidence ExitHardQuestion 20260
Question
For a prism with apex angle A = 30° and n = √3, the minimum angle of incidence for which total internal reflection occurs on the second face is:
- A0° (normal incidence)Correct
- B30°
- C60°
- D45°
Correct answer
0° (normal incidence)
Explanation
Critical angle: sin θ_c = 1/√3 → θ_c ≈ 35.3°. For the ray inside the prism, the angle of incidence at the second surface = A − r₁ where r₁ is the refraction angle at first surface. At normal incidence (i = 0°): r₁ = 0°, angle at 2nd face = A = 30° < θ_c (35.3°) → no TIR at normal incidence. For TIR: r₂ > θ_c → A − r₁ > 35.3°. For A = 30°, A < θ_c, so TIR cannot occur for any angle of incidence for this prism — the condition here doesn't lead to TIR at 0° incidence.