PhysicsCalcs
Optics

Snell’s Law Calculator

Calculate refraction angles, critical angles, and refractive indices using n₁ sin θ₁ = n₂ sin θ₂.

Interactive calculator

Snell's Law Calculator

Calculate refraction angle, incident angle, refractive index, and critical angle using Snell's law: n₁ sin θ₁ = n₂ sin θ₂.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Select what to solve: refraction angle, incident angle, n, or critical angle.
  • Use presets for common material pairs.
  • TIR is automatically detected and explained.

Table of Contents

Key Takeaways

  • Snell's law: n₁ sin θ₁ = n₂ sin θ₂ governs how light bends at material boundaries.
  • Light bends toward the normal when entering a denser medium (higher n).
  • Total internal reflection occurs when light in a denser medium exceeds the critical angle.
  • Critical angle: θ_c = arcsin(n₂/n₁), only exists when n₁ > n₂.
  • Fiber optics rely on TIR: the tiny n difference between core and cladding traps light.

What Is Snell's Law?

Snell’s law (also called the law of refraction) describes how light changes direction when passing from one transparent medium into another. The law relates the angle of incidence, the angle of refraction, and the refractive indices of both media.

Formula

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2
θc=arcsin⁡(n2n1)(n1>n2)\theta_c = \arcsin\left(\frac{n_2}{n_1}\right) \quad (n_1 > n_2)

Total Internal Reflection

When light travels from a denser medium (higher n) to a less dense medium, and the incident angle exceeds the critical angle, no refracted ray exists — all light is reflected. This is the principle behind optical fibers, prisms, and the sparkle of gemstones.

Refractive Indices of Common Materials

MaterialnCritical angle (to air)
Vacuum1.000—
Air1.0003—
Water1.33348.6°
Crown Glass (BK7)1.51741.2°
Flint Glass1.62038.1°
Sapphire1.77034.4°
Diamond2.41724.4°

How to Use

  1. Select what to solve for (refraction angle, incident angle, n, or critical angle).
  2. Enter refractive indices and angles.
  3. Click Calculate — TIR is automatically detected.

Examples

Air → Water at 30°

sin θ₂ = (1.0003/1.333) × sin 30° = 0.375 → θ₂ = 22.0°

Diamond critical angle

θ_c = arcsin(1/2.417) = 24.4° — explains diamond’s fire

FAQ

What happens at the critical angle?›

At the critical angle, the refracted ray travels along the interface (θ₂ = 90°). For any incident angle greater than this, total internal reflection (TIR) occurs — all light is reflected back into the denser medium with zero transmission.

Why does diamond sparkle so much?›

Diamond has a very high refractive index (n = 2.42), giving it a critical angle of only 24.4° with air. This means light entering the diamond gets trapped by TIR at most internal facets, bouncing around before exiting — creating the characteristic sparkle and fire.

Does Snell's law work for all types of light?›

Snell's law applies to all electromagnetic waves, not just visible light. However, the refractive index varies with wavelength (dispersion), so different colors refract at slightly different angles. This is why prisms split white light into a rainbow.

How is Snell's law related to the speed of light?›

The refractive index is the ratio of light speed in vacuum to light speed in the medium: n = c/v. Snell's law is fundamentally about the change in light speed at an interface, which causes the wavefronts to bend.

Sources

  1. Hecht, E. – Optics (5th ed.)
  2. HyperPhysics – Snell's Law
  3. Wikipedia – Snell's Law
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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