Total Internal Reflection: Fibres, Diamonds & Mirage

Total internal reflection is not just a textbook effect. It makes modern communication possible, gives diamonds their fire, and creates mirages that look like water on a dry road. All three phenomena share the same physics: light trapped or bent by changing refractive index.

Understanding these applications shows why critical angle matters in engineering and nature. From internet cables under oceans to desert illusions, the same Snell law explains what we see.

Key Concepts

Optical fibre: Thin glass core with higher n surrounded by cladding with lower n. Light entering at suitable angle reflects repeatedly and travels along fibre, even around bends.

Critical angle for diamond: Diamond has n about 2.42, so C = arcsin 1 divided by 2.42, about 24.4 degrees, very small. This traps most light inside.

Mirage: Hot air near ground has lower n than cooler air above. Light from sky bends gradually and undergoes total internal reflection, creating illusion of water.

• Fibre uses step or gradual change in n to guide light
• Diamond cut angles are designed to exceed C for most internal rays
• Mirage needs temperature gradient, not a flat surface

How It Works

1. In a fibre, light enters core (n about 1.48) surrounded by cladding (n about 1.46). Small difference still gives critical angle near 80 degrees from normal, meaning shallow rays reflect.
2. Each bounce preserves angle, so signal travels kilometres with little loss, carrying data as pulses.
3. In diamond, facets are cut so light entering top hits back facets above C, reflects twice, and exits top toward eye, splitting into colours.
4. In mirage, rays from sky go through warmer, rarer air layers, bend away from normal, curve upward after total internal reflection, and reach eye as if reflected from ground.

The mechanism is same — denser to rarer with angle beyond critical — but geometry differs: fibre is cylindrical, diamond is faceted, atmosphere is layered.

Worked Example

For a fibre core n1 = 1.50 and cladding n2 = 1.47, find critical angle at core-cladding boundary.

1. Use sin C = n2 divided by n1 = 1.47 divided by 1.50 = 0.98.
2. C = arcsin 0.98 = 78.5 degrees from normal.
3. That means rays hitting boundary at more than 78.5 degrees from normal, or less than 11.5 degrees to surface, stay inside.

This high C allows gentle bends in cable without light escaping. Data can travel with reflections every few millimetres yet low loss over long distance.

Common Misconceptions

• Fibres work by simple reflection like mirror: They rely on total internal reflection at core-cladding interface, not metallic coating. No silver is used.
• Diamond sparkles because it is shiny outside: Sparkle comes from internal trapping and dispersion. Poor cut leaks light from bottom and looks dull.
• Mirage is reflection from hot ground: It is refraction plus total internal reflection in air layers. No actual water or mirror surface exists.

Real-World Applications

• Broadband internet, telephone and medical endoscopes use fibre bundles to carry light signals
• Gem cutting maximises brilliance by controlling facet angles relative to critical angle
• Highway mirages on summer days and desert inferior mirages demonstrate atmospheric optics
• Prism systems in cameras and binoculars replace mirrors with total internal reflection for brighter images

Fibres, diamonds and mirages all showcase total internal reflection in different settings. Small critical angle traps light in diamond, layered air bends sky light into a mirage, and engineered fibres guide light for communication.