Snell's Law Calculator

n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.

Inputs

Result

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How to use this calculator

  • Enter n₁, incidence angle, n₂.
  • Read θ₂ or "TIR".

About this calculator

Snell's law (1621): light bends when crossing media with different refractive indices. n₁ sin θ₁ = n₂ sin θ₂. Light slows in denser media (higher n): vacuum 1.000, air 1.0003, water 1.33, glass 1.50, diamond 2.42. Going from denser to less dense (n₁ > n₂), beyond a critical angle (sin θ_c = n₂/n₁), refraction fails — total internal reflection. Underlies fiber-optic cables, prism-spectroscopy, mirages.

Frequently asked

Why "total" internal reflection?+
When n₁ > n₂ and θ₁ > θ_c, sin θ₂ would be > 1 — physically impossible. All light reflects back instead.
Fiber-optic uses?+
Cladding has lower n than core. Light bouncing inside via TIR loses ~0.2 dB/km. Long-distance internet backbone.
Why diamond sparkles?+
High n (2.42) → small critical angle (24°). Most light entering bounces internally many times before exiting.
Snell at θ=0?+
Normal incidence: no bend (sin 0 = 0). Light passes straight through any interface.
Negative refraction?+
Possible with metamaterials. Standard optics: n always positive, θ on same side as normal.

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