Snell's Law
Calculate how light bends when passing between materials.
The fundamental law of refraction in optics.
The Formula
n₁ × sin(θ₁) = n₂ × sin(θ₂)
Snell's law describes how light changes direction when it passes from one medium to another. The bending occurs because light travels at different speeds in different 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) |
Example 1
Light enters water (n=1.33) from air (n=1.00) at 45°. Find the refraction angle.
1.00 × sin(45°) = 1.33 × sin(θ₂)
sin(θ₂) = 0.7071 / 1.33 = 0.5317
θ₂ = arcsin(0.5317) ≈ 32.1°
Example 2
Light enters glass (n=1.52) from air at 30°. Find the refraction angle.
1.00 × sin(30°) = 1.52 × sin(θ₂)
sin(θ₂) = 0.5 / 1.52 = 0.3289
θ₂ = arcsin(0.3289) ≈ 19.2°
When to Use It
Use Snell's law when:
- Calculating how light bends at the boundary between two materials
- Designing lenses, prisms, and optical fibers
- Finding the critical angle for total internal reflection
- Understanding why objects appear shifted underwater