Snell's Law Formula
Snell's Law calculates refraction of light between media: n1 sin(a1) = n2 sin(a2).
Includes total internal reflection and examples.
The Formula
Snell's Law describes how light bends when passing from one medium to another. The amount of bending depends on the refractive indices of the two materials.
Variables
| Symbol | Meaning |
|---|---|
| n₁ | Refractive index of the first medium |
| θ₁ | Angle of incidence (measured from the normal) |
| n₂ | Refractive index of the second medium |
| θ₂ | Angle of refraction (measured from the normal) |
Common Refractive Indices
| Material | Refractive Index (n) |
|---|---|
| Vacuum | 1.000 |
| Air | 1.0003 |
| Water | 1.333 |
| Glass (crown) | 1.52 |
| Diamond | 2.42 |
Example 1
Light enters water from air at a 45° angle. What is the angle of refraction?
n₁ = 1.0003 (air), θ₁ = 45°, n₂ = 1.333 (water)
sin(θ₂) = n₁ × sin(θ₁) / n₂
sin(θ₂) = 1.0003 × sin(45°) / 1.333 = 1.0003 × 0.7071 / 1.333
sin(θ₂) = 0.5306
θ₂ ≈ 32.0° (the light bends toward the normal as it enters the denser medium)
Example 2
Find the critical angle for total internal reflection when light goes from glass (n = 1.52) to air.
At the critical angle, θ₂ = 90°, so sin(θ₂) = 1
sin(θc) = n₂ / n₁ = 1.0003 / 1.52
sin(θc) = 0.6581
θc ≈ 41.1° (any angle greater than this causes total internal reflection)
When to Use It
Use Snell's Law for optics and light refraction problems:
- Designing lenses for glasses, cameras, and telescopes
- Understanding why objects look bent or distorted in water
- Calculating fiber optic light transmission (total internal reflection)
- Analyzing prisms and rainbows (light dispersion)