---
title: "Total Internal Reflection, Optical Fibres and Dispersion"
description: "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 "
canonical: https://lightmysky.com/learn/science/total-internal-reflection-optical-fibres-and-dispersion-mt_ZNSZMLkOD_
source: https://lightmysky.com/learn/science/total-internal-reflection-optical-fibres-and-dispersion-mt_ZNSZMLkOD_.md
retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Waves, Light & Sound · Ages 19 to 20
Page: https://lightmysky.com/learn/science/total-internal-reflection-optical-fibres-and-dispersion-mt_ZNSZMLkOD_

## Ready when they can

- 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

## Lesson: Trapped light and spread colours

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.

**Example.** 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.

**Tip.** 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.

**Recap.** Past the critical angle light is fully trapped, fibres exploit that, and dispersion spreads colours and smears pulses.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Huygens's Principle and the Laws of Reflection and Refraction](https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w)