Snell's Law Calculator
Calculate the angle of refraction using Snell's law: n₁sinθ₁ = n₂sinθ₂. Enter the refractive indices and angle of incidence. Detects total internal reflection and calculates the critical angle.
How to use this tool
- Enter refractive index n₁, angle of incidence θ₁ and refractive index n₂ in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your angle of refraction θ₂ and the full breakdown beneath it.
Snell's law describes refraction: n₁sin(θ₁) = n₂sin(θ₂). When light passes from a denser medium (n₁ > n₂) at a large enough angle, it cannot escape — total internal reflection occurs above the critical angle θ_c = arcsin(n₂/n₁).
Formula
n1 sinθ1 = n2 sinθ2
Solving for refracted angle: θ2 = arcsin(n1 sinθ1 / n2)
Critical angle (when n1 > n2): θc = arcsin(n2 / n1)
How it works
Snell's law describes how light changes direction when crossing a boundary between two media of different refractive indices. The calculator converts the incidence angle to radians, computes sinθ2 = n1sinθ1/n2, and returns the angle in degrees. If |sinθ2| exceeds 1, total internal reflection occurs and no refracted ray exists.
When n1 > n2 (denser-to-less-dense medium), a critical angle is also calculated. Results are rounded to 4 decimal places. The formula assumes monochromatic light at a flat interface; dispersion (wavelength-dependent n) is not modelled.
Worked example
Worked example (air to glass)
- Given: n₁ = 1.0 (air), θ₁ = 30°, n₂ = 1.5 (glass).
- Compute sinθ₂ = n₁ × sin(30°) / n₂ = 1.0 × 0.5 / 1.5 = 0.3333.
- θ₂ = arcsin(0.3333) ≈ 19.4712°.
- Since n₁ < n₂, no total internal reflection occurs and no critical angle applies.
Angle of refraction θ₂ = 19.4712°.
Key terms
- Refractive index (n)
- A dimensionless number indicating how much slower light travels in a medium compared to a vacuum. Air ≈ 1.0003; glass ≈ 1.5.
- Angle of incidence (θ₁)
- The angle between the incoming light ray and the normal (perpendicular) to the interface surface.
- Angle of refraction (θ₂)
- The angle between the refracted ray in the second medium and the normal to the interface.
- Total internal reflection
- A phenomenon where light traveling from a denser to a less dense medium is completely reflected back if the incidence angle exceeds the critical angle.
- Critical angle (θ)
- The minimum angle of incidence (when n₁ > n₂) at which total internal reflection occurs; equal to arcsin(n₂/n₁).
Frequently asked questions
- What is total internal reflection?
- When light in a denser medium (e.g. glass) hits the boundary at an angle greater than the critical angle, all light is reflected back. This is the principle behind fibre-optic cables.
- What are common refractive indices?
- Vacuum/air: 1.0, water: 1.33, crown glass: 1.52, diamond: 2.42.