Snell's Law Calculator

Calculate the angle of refraction using Snell's Law (n₁sinθ₁ = n₂sinθ₂). Find refracted angle, total internal reflection critical angle, Brewster's angle, and fiber optic numerical aperture.

Angle of Refraction θ₂ (degrees)
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Bend Direction —
Critical Angle (if applicable, degrees) —
Brewster's Angle θ_B (degrees) —
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θ₂ Refraction (degrees)
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Status —
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Refraction

θ₂ Refraction (degrees) —
TIR Status —

Special Angles

Critical Angle (degrees) —
Brewster's Angle θ_B (degrees) —

Fiber Optics

Fiber Optic NA —
Fiber Acceptance Half-Angle (degrees) —

How to Use This Calculator

  1. Enter n₁ (refractive index of the first medium, e.g. 1.0003 for air).
  2. Enter θ₁ (angle of incidence in degrees, measured from the normal).
  3. Enter n₂ (refractive index of the second medium).
  4. Results show θ₂, bend direction, critical angle (if n₁ > n₂), and Brewster's angle.
  5. Use the Total Internal Reflection tab to check if TIR occurs at a given angle.

Formula

Snell's Law: n₁ sin θ₁ = n₂ sin θ₂

Critical Angle: θ_c = arcsin(n₂/n₁) (only when n₁ > n₂)

Brewster's Angle: θ_B = arctan(n₂/n₁)

Fiber NA = √(n₁² − n₂²)

Example

Example: Light from glass (n₁ = 1.50) hits water (n₂ = 1.33) at θ₁ = 45°. sin θ₂ = (1.50 × sin 45°) / 1.33 = 0.798. θ₂ = 52.9°. Critical angle = arcsin(1.33/1.50) = 62.5° — TIR does not occur here.

Frequently Asked Questions

  • Snell's Law states n₁sinθ₁ = n₂sinθ₂, relating the angles of incidence and refraction to the refractive indices of the two media. When light crosses a boundary, it bends toward the normal when entering a denser medium and away when entering a less dense medium.
  • When light travels from a denser medium to a less dense medium at an angle greater than the critical angle θ_c = arcsin(n₂/n₁), no refracted ray exists — all light reflects back. This is the principle behind fiber optic cables.
  • Brewster's angle θ_B = arctan(n₂/n₁) is the angle at which reflected light becomes perfectly polarized (only s-polarization reflects, p-polarization is fully transmitted). Used in polarized sunglasses and laser optics.
  • Air: 1.0003, Ice: 1.31, Water: 1.33, Ethanol: 1.36, Quartz: 1.46, Crown glass: 1.52, Diamond: 2.42. Higher n means light travels slower in that medium.
  • NA = √(n_core² − n_cladding²) = n_core × sin(θ_c). It defines the acceptance cone of a fiber — the maximum angle at which light can enter and still undergo total internal reflection along the fiber.

Related Calculators

🌀 Critical Angle Calculator 💎 Refractive Index Calculator 👓 Thin Lens Calculator 🌊 Wavelength Calculator
Sources & References (5) ▾
  1. Snell's Law — HyperPhysics — Georgia State University
  2. MIT OCW 8.03 Vibrations and Waves — MIT OpenCourseWare
  3. OpenStax University Physics Vol 3, Ch 1.4 — Refraction — OpenStax
  4. Hecht, E. Optics (5th ed.) — Pearson
  5. NIST Refractive Index of Common Materials — NIST