Snell's Law Calculator

Find the refraction angle and critical angle when light crosses a boundary.

Inputs

°
Formulas
n₁·sinθ₁ = n₂·sinθ₂
θc = arcsin(n₂ / n₁)

Results

Angle of refraction °
Critical angle °

Snell's law of refraction

When light passes from one transparent medium into another, it bends. Snell's law relates the angles to the refractive indices: n₁sinθ₁ = n₂sinθ₂. Light slows down and bends toward the normal when entering a denser medium, and speeds up and bends away when entering a less dense one.

n₁·sinθ₁ = n₂·sinθ₂

Total internal reflection

When light travels from a denser to a rarer medium, there is a critical angle beyond which it cannot escape and is instead totally internally reflected. The critical angle is arcsin(n₂/n₁), and exists only when n₁ is greater than n₂. This effect makes optical fibres and diamonds work. The calculator shows a dash when no critical angle exists.

Frequently asked questions

What is the refractive index?

It is the ratio of the speed of light in vacuum to its speed in the medium. A higher index means light travels more slowly and bends more.

When does total internal reflection happen?

Only when light moves from a denser to a less dense medium and the angle of incidence exceeds the critical angle.

Read the full guide