Total Internal Reflection and Optical Fibres

When light travels from a denser medium to a less dense medium at an angle greater than the critical angle, it is completely reflected back — this is total internal reflection (TIR). TIR is the principle behind optical fibres used in telecommunications and medicine.

Refraction — A Quick Recap

When light moves from a denser medium (e.g. glass) into a less dense medium (e.g. air), it bends away from the normal (the imaginary perpendicular line).

As the angle of incidence increases, the refracted ray bends further away from the normal.

The Critical Angle

At a certain angle — the critical angle — the refracted ray travels along the boundary (90° to the normal).

For glass to air, the critical angle is approximately 42°.

Total Internal Reflection (TIR)

If the angle of incidence exceeds the critical angle, no refraction occurs. The light is completely reflected back into the denser medium.

Conditions for TIR:

Light must travel from a denser to a less dense medium.
The angle of incidence must be greater than the critical angle.

Note

TIR is called total because 100% of the light is reflected — unlike ordinary reflection where some light is always transmitted.

Optical Fibres

An optical fibre is a very thin glass or plastic strand. Light entering at one end hits the glass-air boundary at an angle greater than the critical angle, so it undergoes TIR repeatedly and travels along the fibre.

Uses of optical fibres:

Telecommunications: transmitting internet and phone signals as pulses of light — faster and carries more data than copper cables.
Medicine (endoscopy): doctors use flexible fibres to look inside the body (e.g. examining the stomach).
Decorative lighting: each fibre carries light to its tip.

Real world: Optical fibres for internet broadband

Broadband internet to your home travels as pulses of light through glass optical fibres no thicker than a human hair. Each time a pulse hits the inner glass wall at more than 42° (the critical angle for glass-air), TIR bounces it forward with virtually no energy loss. This allows signals to travel hundreds of kilometres without needing amplification — and at nearly the speed of light.

Real world: Endoscopy in medicine

During a gastroscopy (stomach examination), a doctor passes a bundle of flexible optical fibres down a patient's throat. Light travels along the fibres via TIR to illuminate the stomach lining, while reflected light travels back up separate fibres to a camera — allowing the inside of the body to be viewed without surgery.

Real world: Diamond sparkle

A diamond's exceptional sparkle comes from TIR. Diamond has a very high refractive index (n = 2.42), giving a very small critical angle of about 24°. Light entering the diamond bounces repeatedly off internal faces by TIR before finally escaping, creating intense flashes of colour and brilliance.

Tip Where do you see this in real life? Broadband cables under the ocean, medical endoscopes, decorative fibre-optic lamps, and even the sparkle of a diamond — all rely on total internal reflection!

Practice Problems

What are the two conditions needed for total internal reflection?

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1. Light must travel from a denser medium into a less dense medium. 2. The angle of incidence must be greater than the critical angle.

Why does TIR not happen when light goes from air into glass?

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TIR only happens when light moves from a denser medium to a less dense medium. Air is less dense than glass, so light going air → glass refracts (bends towards the normal) and does not undergo TIR.

Give one use of optical fibres and explain why TIR makes it possible.

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Example: Internet telecommunications. Light signals bounce along the optical fibre via TIR — each time the light hits the glass-air boundary inside the fibre at more than the critical angle, it is totally reflected, so the signal travels along the fibre with very little loss.