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Fibre Optics

Simple Explanation

An optical fibre carries light over long distances by total internal reflection — light striking the core's boundary at an angle steeper than the critical angle reflects perfectly, bouncing along inside the fibre without escaping.

Why Do We Need It?

Fibre optics carries the modern internet's data as pulses of light, transmitting information over enormous distances with far less signal loss than electrical cables.

Formula

Critical Angle for Total Internal Reflection

θc = sin⁻¹(1/n)

Light traveling inside an optical fibre's core reflects perfectly off the core-cladding boundary (total internal reflection) whenever it strikes at an angle steeper than this critical angle — trapping the light inside the fibre.

θc: — critical angle, in degrees
n: — refractive index of the fibre core relative to the surrounding medium (dimensionless)

When to use it: Whenever the critical angle for total internal reflection inside an optical fibre needs to be found from its core's refractive index.

Worked Example

Find an optical fibre's critical angle

An optical fibre's core has a refractive index of 1.5 (relative to the air outside). Find its critical angle.

Why Does This Work?

As the angle of incidence increases, the refracted ray bends farther from the normal — at the critical angle, the refracted ray grazes exactly along the boundary itself (a 90° refraction angle); at any steeper angle, no refraction is even geometrically possible, so all the light reflects back internally instead.

Real-Life Example

Endoscopes used in medical imaging

A doctor uses a thin, flexible endoscope — a bundle of optical fibres — to see inside a patient's body without invasive surgery.

Light (and the image it carries) bounces along each fibre by total internal reflection, following every bend and curve of the flexible bundle without escaping or being lost.

Practice

An optical fibre has a core refractive index of 2.0. Find its critical angle.

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Common mistake

Assuming total internal reflection happens at ANY angle inside the fibre — it only happens for angles STEEPER than the critical angle; light hitting the boundary at a shallower angle simply refracts out and is lost.

Quick Review

θc = sin⁻¹(1/n).
Beyond the critical angle, light reflects perfectly (total internal reflection).
The basis of fibre-optic communication and medical endoscopes.