Snell's Law Calculator
The angle light bends to when it crosses between two materials — with the critical angle beyond which it reflects instead.
Light slows in denser materials, and the change in speed bends the ray: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index.
How the snell's law calculator works
Light slows in denser materials, and the change in speed bends the ray: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index. Going into a denser medium the ray bends towards the normal; coming out it bends away.
Going from dense to less dense there is a limit. Past the critical angle, arcsin(n₂ ÷ n₁), no refracted ray is possible and the light reflects entirely — total internal reflection. That is what keeps light inside an optical fibre and why a diamond, with its very high index and small 24° critical angle, traps and returns so much light.
Formula: n₁ sin θ₁ = n₂ sin θ₂; critical angle = arcsin(n₂ ÷ n₁)
Worked examples
| Inputs | Angle of refraction | Note |
|---|---|---|
| Air into water at 45° | 32.1176 ° | refracts to 32.12° |
| Water into air at 60° — beyond critical | — | total internal reflection |
| Air into glass at 30° | 19.4712 ° | 19.47° |
FAQFrequently asked questions
What is Snell's law?
n₁ sin θ₁ = n₂ sin θ₂ — it relates the angles a light ray makes either side of a boundary to the refractive indices.
Why does light bend?
Because it travels slower in denser materials. The change in speed across the boundary turns the wavefront.
What is the critical angle?
The incidence angle beyond which light cannot leave a denser medium at all and reflects entirely. For water to air it is 48.75°.
How do optical fibres work?
Total internal reflection — light hits the core-cladding boundary beyond the critical angle every time, so it stays trapped along the fibre.
Why do diamonds sparkle?
A refractive index of 2.42 gives a critical angle of just 24°, so most light entering is reflected repeatedly inside before leaving.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.