Refraction Calculator

Calculate refractive index, angle of refraction, and critical angle using Snell's Law

Input Values

Result

What is Refraction?

Refraction is the change in direction of a wave passing from one medium to another caused by its change in speed. This phenomenon is commonly observed when light passes from air into water or glass, causing the light to bend.

Snell's Law

The fundamental law governing refraction is Snell's Law:

n₁ × sin(θ₁) = n₂ × sin(θ₂)

Where:

  • n₁ = Refractive index of first medium
  • θ₁ = Angle of incidence (degrees)
  • n₂ = Refractive index of second medium
  • θ₂ = Angle of refraction (degrees)

Critical Angle

The critical angle is the angle of incidence beyond which total internal reflection occurs:

θc = arcsin(n₂/n₁)

Common Refractive Indices

MaterialRefractive Index
Air1.0003
Water1.33
Glass (Crown)1.52
Glass (Flint)1.66
Diamond2.42

How to Use the Calculator

  1. Choose what you want to calculate (angle of refraction, refractive index, or critical angle)
  2. Enter the known values in the appropriate fields
  3. Click "Calculate" to get the result
  4. View the step-by-step solution

Example Calculation

Light passes from air (n₁ = 1.00) to water (n₂ = 1.33) at an angle of incidence of 30°:

n₁ × sin(θ₁) = n₂ × sin(θ₂)

1.00 × sin(30°) = 1.33 × sin(θ₂)

0.5 = 1.33 × sin(θ₂)

sin(θ₂) = 0.5/1.33 = 0.376

θ₂ = arcsin(0.376) = 22.1°