Snell's law describes how light bends when passing between media of different densities, such as from air into water or glass. This bending (refraction) is why a straw in water appears bent and why lenses focus light. Understanding refraction is essential for optics, lens design, and understanding phenomena like mirages and rainbows.
The Formula
n₁ × sin(θ₁) = n₂ × sin(θ₂)
Where:
- n₁ = refractive index of first medium
- θ₁ = angle of incidence (from the normal)
- n₂ = refractive index of second medium
- θ₂ = angle of refraction (from the normal)
Angles are always measured from the normal (perpendicular) to the surface, not from the surface itself.
Common Refractive Indices
| Medium | Refractive Index |
|---|---|
| Vacuum | 1.0 |
| Air | 1.0003 ≈ 1.0 |
| Water | 1.33 |
| Glass | 1.5 – 1.9 |
| Diamond | 2.42 |
Higher refractive index means light travels slower in that medium.
Worked Example
Light travels from air (n=1.0) into water (n=1.33) at an incident angle of 45°.
1.0 × sin(45°) = 1.33 × sin(θ₂)
sin(θ₂) = sin(45°) / 1.33 = 0.707 / 1.33 = 0.531
θ₂ = arcsin(0.531) = 32.1°
Light bends toward the normal when entering a denser medium. The refracted ray is closer to the normal (32.1°) than the incident ray (45°).
Critical Angle and Total Internal Reflection
When light travels from a denser to a less dense medium (e.g., glass to air), there's a critical angle beyond which light doesn't refract out but instead reflects back entirely. This is total internal reflection:
sin(θc) = n₂ / n₁
For glass (n=1.5) to air (n=1.0):
θc = arcsin(1.0 / 1.5) = 41.8°
Incident angles greater than 41.8° cause total internal reflection. This principle enables fiber optics to trap light.
Applications
Lenses: Lens shape and refractive index work together to focus or diverge light. Stronger refraction (higher n) means thinner lenses can achieve the same focal length.
Prisms: Refraction at different wavelengths (dispersion) separates white light into a spectrum.
Fiber Optics: Total internal reflection contains light signals within optical fiber cables.
Tips
Always measure angles from the normal, not the surface. When light enters a denser medium, it bends toward the normal. When exiting a denser medium, it bends away from the normal. This asymmetry is why swimming pools appear shallower than they are.
Use our Snell's Law Refraction Calculator to find refraction angles instantly.