Total Internal Reflection & Optical Fibres
Past a certain angle, glass becomes a perfect mirror, and that is how fibres carry light.
Lesson at a glanceShow the key points
- From denser to rarer medium the ray bends away from the normal; at the critical angle θc the refracted ray grazes the surface (r = 90°).
- Beyond θc no refraction is possible: all the light reflects back, total internal reflection.
- Into air: sin θc = 1/μ (18.7).
- An optical fibre is a thin glass or plastic thread; light inside hits its wall beyond θc and is trapped, even round bends.
- Uses: viewing inside the body (light pipes), and carrying many telephone signals at once. Each fibre is coated with a lower-index layer to insulate it optically.
Look up at the surface of a swimming pool from underwater and, beyond a certain angle, it shines like a silver mirror. Glass and water can reflect perfectly, without any silvering at all.
The critical angle
When light passes from an optically denser medium (larger μ) into a rarer one (smaller μ), it bends away from the normal: the angle of refraction r is bigger than the angle of incidence i.
Increase i and r grows faster. At one angle of incidence, the critical angle θc, the refracted ray skims along the surface (r = 90°). For larger i, no angle r can satisfy Snell’s law: there is no refracted ray at all, and all the light reflects back into the denser medium. This is total internal reflection.
Usually the critical angle is quoted for light going from a medium into air. Putting μ₂ = 1 and r = 90° in Snell’s law:
The critical angle for diamond is 24.4°. Find its refractive index.
What is the critical angle for glass of refractive index 1.5?
Optical fibres
An optical fibre is a very thin thread of glass or plastic, only micrometres across. Light sent into one end strikes the wall at a very glancing angle, far beyond the critical angle, and is totally reflected. It bounces along inside the fibre, even round bends, with almost no loss. A bundle of fibres is a light pipe.
Uses
- Seeing inside the body: a light pipe is passed down into, say, the stomach. Some fibres carry light in; others carry the image back out to the viewer.
- Communication: thousands of telephone signals, mixed into the light, can travel along one fibre at once, far more clearly than in ordinary cables.
- 1From denser to rarer, a ray bends away from the normal; at the critical angle it grazes the surface.
- 2Beyond θc all the light is reflected: total internal reflection.
- 3Into air: sin θc = 1/μ (glass ≈ 42°, water ≈ 49°, diamond ≈ 24°).
- 4Optical fibres trap light by total internal reflection; they are coated with a lower-index layer. Used in medicine and communication.
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Keep exploring
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