--- title: "Total Internal Reflection, Optical Fibres and Dispersion" description: "At an ideal boundary from higher to lower refractive index, incidence above the critical angle gives total internal reflection. This guides suitable light in fibres. Wavelength-dependent refraction se" 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: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Total Internal Reflection, Optical Fibres and Dispersion At an ideal boundary from higher to lower refractive index, incidence above the critical angle gives total internal reflection. This guides suitable light in fibres. Wavelength-dependent refraction separates prism colours, while modal and chromatic dispersion can broaden fibre pulses. 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 Recall Snell's law: n1 sin θ1 = n2 sin θ2, with angles from the normal. Let light reach an isolated boundary from index n1 toward n2, where n1 > n2. The transmitted ray bends away from the normal. At critical incidence θc, its limiting angle is 90 degrees. Above θc, there is no propagating transmitted ray across the boundary. This is total internal reflection in the ideal transparent, nonabsorbing model. **Example.** Set θ2 = 90 degrees in Snell's law. Since sin 90 degrees = 1, sin θc = n2 ÷ n1. Thus θc = arcsin(n2 ÷ n1), for n1 > n2. Use degree mode on a calculator. Given n1 = 1.60 and n2 = 1.20, the ratio is 0.75 and θc is about 48.6 degrees. *(drawing: These cases require n1 > n2. The cells compare conditions; they do not draw rays or measured angles.)* A step-index fibre has a higher-index core surrounded by lower-index cladding. In the ray model, rays meeting the core boundary above its critical angle are guided by repeated total internal reflection. The index step permits guidance but does not trap every launch direction. Absorption, scattering and excessive bending can still reduce the signal. Prism dispersion depends on wavelength: the index varies with wavelength, so Snell's law gives different refraction directions. In ordinary transparent glass with normal dispersion across visible wavelengths, blue has a higher index than red and a greater total prism deflection. That ordering is not universal across materials and wavelengths. Modal dispersion in a fibre instead comes from different guided-mode travel times, even at the same wavelength. In a multimode fibre, guided paths or modes can have different travel times: modal dispersion. Chromatic dispersion gives different wavelength components different pulse travel times. Pulse envelopes travel at group velocity; c ÷ n gives phase speed. Timing spread can broaden pulses until neighbouring signals overlap, limiting data rate. Broadening does not prove leakage. Single-mode operation removes modal dispersion, but chromatic dispersion can remain. The normal is perpendicular to the surface. An acute angle α from the surface gives incidence θ = 90 degrees - α. For example, 25 degrees from the surface is 65 degrees from the normal. Compare this normal angle with θc. Equality gives the limiting refracted angle of 90 degrees; total internal reflection requires incidence above θc. **Recap.** Total internal reflection needs higher-to-lower index and incidence above θc, with sin θc = n2 ÷ n1. Fibres guide suitable light. Dispersion can separate colours or broaden pulses. *Lesson, questions and flashcards written for this learning dataset.* ## 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)