Critical Angle Calculator

How to Use This Calculator

1. Enter n₁ (the denser medium — must be greater than n₂ for TIR to occur).
2. Enter n₂ (the less dense medium, default air = 1.0003).
3. Results show the critical angle, TIR status, and fiber optic NA.
4. Use TIR Check tab to test a specific incident angle.
5. Use Common Pairs for glass-air, water-air, diamond-air presets.

Formula

Example

Frequently Asked Questions

• What is the critical angle? ▼
  θ_c = arcsin(n₂/n₁), where n₁ > n₂. When light in a denser medium hits a less dense medium at θ ≥ θ_c, no refracted ray exists — all light reflects back (total internal reflection). For glass-air (n₁=1.5): θ_c ≈ 41.8°.
• Why does TIR require n₁ > n₂? ▼
  Snell's Law: n₁ sin θ₁ = n₂ sin θ₂. If n₁ > n₂, as θ₁ increases, sin θ₂ = (n₁/n₂) sin θ₁ can exceed 1 — which is impossible. The critical angle is where sin θ₂ = 1, so θ₂ = 90° (refracted ray grazes the surface).
• How does TIR work in fiber optic cables? ▼
  Fiber cores (n ≈ 1.48) are surrounded by cladding (n ≈ 1.46). Light entering within the acceptance cone bounces along the fiber via TIR with virtually no loss. NA = √(n_core² − n_clad²) defines the acceptance angle.
• What is numerical aperture (NA) in fiber optics? ▼
  NA = n_medium × sin(θ_max) = √(n_core² − n_cladding²). Larger NA = wider acceptance cone = easier to couple light in, but more modal dispersion. Typical single-mode fiber: NA ≈ 0.12. Multi-mode: NA ≈ 0.20–0.50.
• What is the critical angle for diamond? ▼
  Diamond (n = 2.417) vs air: θ_c = arcsin(1/2.417) ≈ 24.4°. This very small critical angle means most light entering a diamond undergoes multiple TIR reflections before exiting — the source of diamond's brilliance.

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