Science & Engineering
Snell's Law Calculator - Refraction Angle & Total Internal Reflection
Solve Snell's Law n₁sin(θ₁) = n₂sin(θ₂) for the refracted angle or refractive index. Automatically detects total internal reflection and shows the critical angle.
n₁
1.0000
θ₁ (°)
30.00
n₂
1.5000
θ₂ (°)
19.47
Common Refractive Indices
| Medium | n (approx) |
|---|---|
| Vacuum | 1.000 |
| Air (at STP) | 1.0003 |
| Ice | 1.31 |
| Water (20°C) | 1.333 |
| Ethanol | 1.36 |
| Glycerin | 1.47 |
| Crown glass | 1.52 |
| Window glass | 1.52 |
| Quartz (fused silica) | 1.46 |
| Flint glass | 1.62 |
| Polycarbonate (lenses) | 1.586 |
| Ruby | 1.77 |
| Sapphire | 1.77 |
| Zirconia (cubic) | 2.15 |
| Diamond | 2.417 |
Snell's Law formula
When light crosses the boundary between two media, the angle of refraction relates to the angle of incidence by Snell's Law:
n₁ sin(θ₁) = n₂ sin(θ₂)
where n₁ and n₂ are the refractive indices of the first and second media, and θ₁ and θ₂ are the angles measured from the normal (a line perpendicular to the boundary surface). A higher refractive index bends light more toward the normal; a lower refractive index bends it away.
Worked example: air to water
Light travels from air (n₁ = 1.000) into water (n₂ = 1.333) at an angle of incidence of 45°.
sin(θ₂) = (n₁ / n₂) × sin(θ₁) = (1.000 / 1.333) × sin(45°) = 0.7500 × 0.7071 ≈ 0.5303
θ₂ = arcsin(0.5303) ≈ 32.0°
The light bends toward the normal as it enters the denser medium (water).
Total internal reflection
When light travels from a denser medium (high n) to a less dense medium (low n), there is a maximum angle of incidence beyond which all light is reflected rather than refracted. This angle is called the critical angle:
θc = arcsin(n₂ / n₁)
For water to air: θc = arcsin(1.000 / 1.333) ≈ 48.6°. Incidence angles beyond 48.6° produce total internal reflection - no light escapes the water.
Total internal reflection is the principle behind optical fiber (light bounces down a glass core indefinitely) and is why diamonds sparkle - the gem is cut so that entering light undergoes multiple total internal reflections before exiting through the top, concentrating light brilliantly.