Snell's Law Calculator - Refraction Angle & Total Internal Reflection

How to use this tool

1. Enter the refractive index of both media (n1, n2) and the incident angle θ1.
2. View the refracted angle θ2, critical angle, and whether total internal reflection occurs.
3. Or leave n2 blank and enter θ2 to solve for the unknown refractive index.

Common Refractive Indices

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.