Critical Angle for Total Internal Reflection

When light travels from a denser medium (higher n) to a less dense medium (lower n), total internal reflection occurs if the angle of incidence exceeds the critical angle:

θ_c = arcsin(n₂/n₁) where n₁ > n₂

At angles greater than θ_c, ALL light is reflected back — none escapes. This is the basis of optical fiber communication.

Snell’s Law at the critical angle: n₁ sin(θ_c) = n₂ sin(90°) = n₂ → sin(θ_c) = n₂/n₁

Requirements:

• Light must travel from the denser medium (higher n) to the less dense one
• n₁ must be > n₂
• If n₁ < n₂, there is no critical angle — total internal reflection cannot occur in this direction

Common material refractive indices:

• Air/vacuum: n = 1.000
• Water: n = 1.333
• Crown glass: n = 1.52
• Flint glass: n = 1.62
• Diamond: n = 2.417
• Cubic zirconia: n = 2.17

Applications:

• Optical fiber: Light travels in a glass or plastic core (n ≈ 1.5) surrounded by cladding (n ≈ 1.46). Critical angle ≈ 77°. Light bounces along the fiber with essentially zero loss.
• Diamonds: High refractive index (2.417) gives critical angle of only 24.4° — light entering the diamond is totally internally reflected many times before escaping, creating the famous “fire” and brilliance.
• Prisms in binoculars: Roof prisms use total internal reflection to fold the optical path compactly.
• Swimming pools: Viewed from underwater beyond the critical angle, the surface appears like a mirror.