Snell's Law
Reference for Snell's Law n1 sin(θ1) = n2 sin(θ2).
Covers refraction angles for air, glass, and water, plus total internal reflection and critical angle.
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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
Key Notes
- Angles are measured from the normal (the line perpendicular to the surface), not from the surface itself — measuring from the surface is the most common mistake when applying this formula
- Total internal reflection (TIR) occurs when light travels from a denser to a less dense medium and the angle exceeds the critical angle: θ_c = arcsin(n₂/n₁); for glass-to-air this is ~41.8° — the basis for optical fibers
- Snell's law assumes a perfectly flat interface; for curved surfaces (lenses, corneas), it is applied locally at each point along the surface using the normal at that point
- The law applies to any wave crossing a medium boundary — sound in water/air, seismic waves in rock layers, and radio waves in the atmosphere all obey the same refraction relationship