Snell’s Law and Refraction
Refraction and Snell’s law explained: why light bends between materials, refractive index, n₁ sin θ₁ = n₂ sin θ₂, total internal reflection and a calculator.
Key takeaways
- Light bends when it changes speed moving between materials.
- Snell’s law: n₁ sin θ₁ = n₂ sin θ₂.
- Beyond the critical angle, light reflects entirely inside the denser material.
On this page
Put a straw in a glass of water and it looks broken at the surface. That’s refraction: light bending as it passes from one material into another.
Why light bends
Light travels at different speeds in different materials. When it enters a material at an angle and changes speed, it changes direction. The refractive index (n) measures how much a material slows light: n = speed of light in a vacuum ÷ speed in the material.
| Material | Approximate refractive index |
|---|---|
| Air | 1.00 |
| Water | 1.33 |
| Glass | about 1.5 |
| Diamond | about 2.42 |
Snell’s law
n₁ sin θ₁ = n₂ sin θ₂
- θ₁ = angle of incidence (from the normal)
- θ₂ = angle of refraction
Going into a denser material, light bends towards the normal; going into a less dense one, it bends away.
Calculator
Snell’s law calculator
Total internal reflection
When light travels from a denser material to a less dense one at a steep enough angle (beyond the critical angle), it reflects entirely back inside. This makes optical fibres work and gives diamonds their sparkle.
Everyday examples
Lenses in glasses and cameras, pools looking shallower than they are, and rainbows. Polarisation, another property of light, explains why the sky is blue and how screens work.
Frequently asked questions
Why do pools look shallower than they are?
Light from the bottom bends away from the normal as it leaves the water, making the bottom appear higher.
What is the critical angle?
The angle of incidence above which total internal reflection happens. For water to air, it’s about 49°.
Does refraction change light’s frequency?
No. Speed and wavelength change; frequency stays the same.
Sources
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