Refractive Index and Snell's Law Calculator
Calculate the angle of refraction when light passes between two materials.
🔭 Optics📐 n₁ sin θ₁ = n₂ sin θ₂ (Snell's Law)
Refractive index n1
Angle of incidence (°)
Refractive index n2
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| Refractive Index and Snell's Law Calculator | n₁ sin θ₁ = n₂ sin θ₂ (Snell's Law) | degrees |
Step-by-Step Examples
Example 1
Air to Glass
n1=1.0, 45°, n2=1.5 (glass).
- sin(θ2) = 1.0×sin(45°)/1.5 = 0.4714
- θ2 = 28.1°
✓ 28.1°
Example 2
Glass to Air — TIR
n1=1.5, 45°, n2=1.0.
- sin(θ2) = 1.5×sin(45°)/1.0 = 1.06 > 1
- Total internal reflection!
✓ TIR — no refracted ray
Example 3
Water to Air
n1=1.33, 30°, n2=1.0.
- θ2 = arcsin(1.33×sin(30°)) = 41.7°
✓ 41.7°
Real-World Applications
Optics Students
Master Snell's law with real calculations.
Camera Designers
Calculate lens geometry.
Physics Teachers
Demonstrate light refraction.
Gemologists
Understand diamond total internal reflection.
Common Mistakes to Avoid
⚠️
Degrees vs radians
Math functions need radians. sin(45°) = sin(π/4) ≈ 0.707.
⚠️
Partial reflection exists
Some light is always reflected at any interface — not just at TIR.
Frequently Asked Questions
What is refractive index? ▾
n = c/v. Air: ~1.0003. Water: 1.33. Glass: 1.5. Diamond: 2.42. Higher n = slower light.
Total internal reflection? ▾
When light goes from dense to rare medium past the critical angle. Basis of optical fiber communications.
Why diamonds sparkle? ▾
Diamond n=2.42 gives tiny critical angle (24.4°). Light undergoes multiple TIR before exiting.