Snell's Law Calculator
n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.
Result
Refracted angle θ₂
19.4712°
From 30° in n=1 → 19.47° in n=1.5.
- n₁1
- θ₁30°
- n₂1.5
- sin θ₁0.500000
- n₁ sin θ₁0.500000
- sin θ₂0.333333
- θ₂19.4712°
- Critical angle (n₁>n₂)—
Step-by-step
- n₁ sin θ₁ = 1 × 0.5000 = 0.5000.
- sin θ₂ = (n₁ sin θ₁) / n₂ = 0.3333.
- θ₂ = arcsin(0.3333) = 19.4712°.
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
When n₁ > n₂ and θ₁ > θ_c, sin θ₂ would be > 1 — physically impossible. All light reflects back instead.
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