Fibre Optics: Principle of Total Internal Reflection

Fibre optics carries information as pulses of light through hair-thin strands of glass. The trick is total internal reflection: light entering the fibre at a shallow enough angle bounces perfectly off the inner walls thousands of times, trapped inside the core all the way to the other end — even around bends.

This matters because a single fibre pair can carry terabits of data per second with almost no loss, forming the backbone of the internet, phone networks and cable TV. Fibre also enables endoscopes that let doctors see inside the body and sensors that monitor bridges and pipelines.

Key Concepts

• Total internal reflection (TIR): When light in a denser medium hits the boundary above the critical angle, 100% reflects — no transmission, no loss at the bounce.
• Critical angle (θ_c): sin θ_c = n₂/n₁, where n₁ is the core's refractive index and n₂ the cladding's (n₁ > n₂).
• Core and cladding: The light-carrying glass core (higher index) wrapped in cladding (lower index); a protective coating shields both.
• Numerical aperture (NA): NA = √(n₁² − n₂²) = sin θ_a — measures the fibre's light-gathering power; θ_a is the acceptance angle.
• Single-mode vs multimode: Single-mode fibres (thin core, ~9 μm) carry one light path for long distances; multimode (thicker core) carry many paths but only over short distances.
• Attenuation: Signal loss in dB/km; modern fibres lose only ~0.2 dB/km at 1550 nm.

Formulas

Snell's law: n₁·sin θ₁ = n₂·sin θ₂. Critical angle: sin θ_c = n₂/n₁ (measured from the normal). Numerical aperture: NA = √(n₁² − n₂²); acceptance angle θ_a = arcsin(NA). Larger NA means the fibre accepts light from a wider cone — easier coupling but (in multimode) more dispersion.

Worked Example

A fibre has core index n₁ = 1.50 and cladding index n₂ = 1.45. Find the critical angle and numerical aperture.

1. Critical angle: sin θ_c = 1.45/1.50 ≈ 0.9667 → θ_c ≈ 75.2° (from the normal).
2. Any ray hitting the wall at more than 75.2° from the normal is totally reflected.
3. NA = √(1.50² − 1.45²) = √(2.25 − 2.1025) = √0.1475 ≈ 0.384.
4. Acceptance angle: θ_a = arcsin(0.384) ≈ 22.6° — light entering within a 22.6° half-angle cone is captured and guided.

Common Misconceptions

• "Light travels at full speed through fibre." Light in glass slows to about c/n ≈ 200,000 km/s — still fast enough to circle the globe in a fraction of a second.
• "Bending fibre breaks the signal." Gentle bends are fine — TIR keeps working; only sharp kinks let light leak out (bend loss).
• "Fibre carries electricity." It carries light, which is why fibre is immune to electromagnetic interference and lightning, and cannot be tapped without physically disturbing the signal.

Real-World Applications

• Undersea and terrestrial fibre cables carry over 99% of intercontinental internet traffic.
• Medical endoscopes use fibre bundles to image inside the body with minimal invasion.
• Fibre sensors monitor strain, temperature and pressure in bridges, aircraft, oil wells and power grids.

Fibre optics traps light in a glass core by total internal reflection, with the critical angle sin θ_c = n₂/n₁ and light-gathering power NA = √(n₁² − n₂²) — a 1.50/1.45 fibre gives θ_c ≈ 75.2° and NA ≈ 0.384. Nearly lossless, immune to interference and enormously high-capacity, optical fibre is the physical backbone of the modern internet — plus endoscopes, sensors and laser delivery.