What Happens as Angle of Incidence Increases Gradually

Consider light going from glass (denser) to air (rarer).

Stage 1: i < Critical angle • Refracted ray exists in air. • Angle of refraction r > angle of incidence i (bends away from normal). • As i increases → r also increases. • Partial reflection also occurs at the surface.

Stage 2: i = Critical angle (C) • Refracted ray travels exactly along the surface. • Angle of refraction = 90°. • Critical angle for glass-air: C ≈ 42° (n_glass ≈ 1.5) • sin C = n_rarer / n_denser = 1 / n

Stage 3: i > Critical angle • No refracted ray — total internal reflection (TIR). • All light reflects back into the denser medium. • Angle of reflection = angle of incidence (laws of reflection still hold).

Summary: i < C → refraction + partial reflection i = C → refraction along surface (r = 90°) i > C → total internal reflection

At the critical angle, r = 90°: Snell's law: n₁ sin i = n₂ sin r n sin C = 1 × sin 90° = 1 sin C = 1/n

Critical angles for common media (with air): • Glass (n=1.5): C = sin⁻¹(1/1.5) = 41.8° • Water (n=1.33): C = sin⁻¹(1/1.33) = 48.8° • Diamond (n=2.42): C = sin⁻¹(1/2.42) = 24.4° • Ice (n=1.31): C = sin⁻¹(1/1.31) = 49.8°

Higher refractive index → smaller critical angle → TIR occurs more easily. Diamond has a very small critical angle (24.4°), which is why it sparkles so brilliantly.

1. Optical fibres: Light is trapped inside the glass fibre by TIR. Used in telecommunications and endoscopy.

2. Diamonds: Small critical angle (24.4°) causes multiple TIR inside, creating brilliance.

3. Mirage: Hot air near ground has lower refractive index. Light from sky undergoes TIR near ground, creating illusion of water.

4. Periscopes and binoculars: Prisms use TIR to redirect light at 90° or 180°.

5. Sparkling of glass objects: TIR at glass-air surfaces creates shiny appearance.

Conditions for TIR:

1. Light must travel from denser to rarer medium.
2. Angle of incidence must exceed the critical angle.