Snell’s law relates refraction across an interface:
n₁ sin(θ₁) = n₂ sin(θ₂)
where angles are measured from the normal.
- Solve θ₂:
θ₂ = asin((n₁/n₂)·sin θ₁) - Solve θ₁:
θ₁ = asin((n₂/n₁)·sin θ₂) - Solve n₁:
n₁ = n₂·sin θ₂ / sin θ₁ - Solve n₂:
n₂ = n₁·sin θ₁ / sin θ₂
n₁ > n₂ and sin(θ₂) would exceed 1, refraction is not possible.
The critical angle is θc = asin(n₂/n₁).
- Select what you want to solve for (θ₁, θ₂, n₁, or n₂).
- Choose an angle unit and enter the other three values.
- Press Submit to see results below the header.
- If total internal reflection appears, reduce θ₁ or change media.
- Use Download CSV or Download PDF to save outputs.
Common refractive indices and a sample calculation row for reference.
| Material | Approx. refractive index (n) | Notes |
|---|---|---|
| Air | 1.0003 | Varies slightly with conditions |
| Water | 1.333 | Visible light, room temperature |
| Glass (typical) | 1.50 | Depends on composition |
| Acrylic | 1.49 | Often close to common glass |
| Diamond | 2.417 | Very high index for visible light |
| Example | n₁ | n₂ | θ₁ | θ₂ | Comment |
|---|---|---|---|---|---|
| Air → Glass | 1.0003 | 1.50 | 30° | ≈ 19.47° | Bends toward the normal |
1) Are angles measured from the surface or the normal?
Snell’s law uses angles from the normal. If you have surface angles, convert by subtracting from 90° (or π/2) before calculating.
2) What does “total internal reflection” mean here?
It means refraction has no real solution because the required sine exceeds 1. Physically, the wave reflects back into the first medium.
3) Why can’t I solve for n₁ or n₂ when an angle is zero?
Solving for an index divides by sin(θ). When θ is 0, sin(θ)=0, so the equation becomes undefined. Use a nonzero angle to compute indices.
4) Which refractive index values should I use?
Use values appropriate for wavelength and temperature. For quick estimates, air≈1.0003, water≈1.333, and common glass≈1.50.
5) Why does θ₂ sometimes stay much smaller than θ₁?
When n₂>n₁, light slows down and bends toward the normal. The refracted angle increases more slowly, so θ₂ can remain well below θ₁.
6) What is the practical use of Brewster’s angle?
At Brewster’s angle, p-polarized reflection is minimized for ideal dielectrics. It’s used in polarization optics, glare reduction, and laser alignment.