Total Internal Reflection, Optical Fibres and Dispersion
Past the critical angle light cannot leave a dense material at all, which is what keeps a signal inside a fibre. Because refractive index depends on wavelength, a prism spreads white light and a long fibre smears a pulse.
What a learner can do afterwards
- Calculates a critical angle from two refractive indices
- Explains how a step-index fibre guides light and what limits its bandwidth
- Links dispersion in a prism to the wavelength dependence of refractive index
1 · Read
Light moving toward a rarer material bends away from the normal, and past one special angle it cannot get out at all. That critical angle gives a refracted ray running at 90 degrees, and anything steeper reflects fully back inside. With n1 the dense side and n2 the rare side, sine of the critical angle is n2 over n1.
Polystyrene of index 1.49 in air has sine equal to 1 over 1.49, so the critical angle is 42.2 degrees. Water to air gives 48.6 degrees and diamond to air only 24.4 degrees: stronger contrast traps more steeply. A fibre uses the same trick, with a thin high-index core inside lower-index cladding so grazing rays keep reflecting for kilometres.
The index itself shifts with wavelength, which is called dispersion. A prism spreads white light because each colour bends by its own amount. The same shift smears fibre pulses: different wavelengths travel at different speeds, and different ray paths arrive at different times, which caps the bandwidth.
Check both conditions before claiming trapping: the light must start dense and head rare, and the hit must land past the critical angle. Steepness is measured from the normal, not from the surface, so grazing rays along the fibre count as steep hits.
Past the critical angle light is fully trapped, fibres exploit that, and dispersion spreads colours and smears pulses.
2 · Watch
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Where it sits
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Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.