Snell's Law Calculator
Compute refraction or incidence angle from n₁, n₂ and one angle. n₁sinθ₁=n₂sinθ₂. Air→water: 30°→22°; total internal reflection when angle exceeds critical angle.
Input Data
Results
At a glance:Snell's law states n₁sinθ₁=n₂sinθ₂, where n are refractive indices and θ are angles measured from the normal. It quantifies how light bends at an interface. The critical angle θc=arcsin(n₂/n₁) (for n₂<n₁) is the incidence angle beyond which total internal reflection occurs. Properties: (1) light bends toward the normal entering a denser medium; (2) bends away when leaving it; (3) at the critical angle the refracted ray runs along the interface. Applications: (1) camera and eyeglass lenses; (2) optical fibres; (3) prisms and spectrometers; (4) mirages and rainbows; (5) underwater vision.
Formula
Snell's law: n₁·sinθ₁ = n₂·sinθ₂
Critical angle: θc = arcsin(n₂/n₁) (n₂<n₁)
$$n_1 \sin\theta_1 = n_2 \sin\theta_2, \quad \theta_c = \arcsin\frac{n_2}{n_1}$$How to Use
- Enter n₁ and n₂, plus one angle (θ₁ or θ₂).
- The calculator returns the other angle.
- Enable the critical-angle option to find total-internal-reflection threshold.
Case Studies
Optical fibre in Hong Kong telecom
Fibre core n≈1.468, cladding n≈1.462. Critical angle θc=arcsin(1.462/1.468)≈83.3° (from normal).
Light enters near the axis so it strikes the wall above the critical angle and reflects totally, guiding signals for kilometres.
This principle underpins HK's submarine and metro fibre networks.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.