# Waves, superposition and optics: Unit 2.1(d)

> state conditions for total internal reflection and apply the critical-angle relation

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Specification statement (Unit 2.1(d)): state conditions for total internal reflection and apply the critical-angle relation

## Explanation

1. **Total internal reflection** happens only when light travels from a **higher** to a **lower** refractive index **and** the angle of incidence exceeds the **critical angle**.
2. At the critical angle c the refracted ray runs along the boundary (refraction angle 90°). From Snell's law: sin c = n₂/n₁.
3. Optical fibres use a core with a slightly higher refractive index than the cladding, so light hitting the boundary at more than c is totally internally reflected along the fibre.

## Worked example

Find the critical angle for glass (n = 1.50) to air, and for a fibre core of n = 1.48 inside cladding of n = 1.46.

1. Glass to air: sin c = 1.00/1.50 = 0.667, c = 41.8°.
2. Core to cladding: sin c = 1.46/1.48 = 0.986, c = 80.6°.

Answer: 41.8°; 80.6°.

## Check

Which condition is needed for total internal reflection?

- Light moves into a denser medium at any angle
- Light moves into a less dense medium at more than the critical angle
- Light hits the boundary along the normal
- The two media have equal refractive index

The answer and its explanation are shown in the app once you choose an option.

## Apply it

Explain why a cladding is used in optical fibres instead of leaving the glass core surrounded by air.

The model answer is shown in the app after you have tried it.

## Related

- [Waves, superposition and optics lesson](https://revise-gray.vercel.app/lesson?subject=wjec-alevel-physics&topic=wjec-alevel-physics.waves)
- [Waves, superposition and optics in the library](https://revise-gray.vercel.app/library?topic=wjec-alevel-physics.waves)