# Snell's Law Calculator (n₁ sinθ₁ = n₂ sinθ₂)

Calculate refraction angles with Snell's Law (n₁ sinθ₁ = n₂ sinθ₂). Find critical angle for total internal reflection.

## What this calculates

Snell's Law describes how light bends when it passes from one medium to another. The formula n₁ sin(θ₁) = n₂ sin(θ₂) relates the angles of incidence and refraction to the refractive indices of the two media. This calculator also determines the critical angle for total internal reflection, which is the basis for fiber optics and optical instruments.

## Inputs

- **Refractive Index n₁ (medium 1)** — min 1 — Air: 1.00, Water: 1.33, Glass: 1.52, Diamond: 2.42
- **Refractive Index n₂ (medium 2)** — min 1
- **Angle of Incidence (θ₁)** (°) — min 0, max 90

## Outputs

- **Angle of Refraction (θ₂)** (°) — Angle of the refracted ray
- **Critical Angle** (°) — Angle for total internal reflection (only if n₁ > n₂)
- **Total Internal Reflection** — formatted as text — Whether total internal reflection occurs

## Frequently Asked Questions

**Q: What is Snell's Law?**

A: Snell's Law (n₁ sinθ₁ = n₂ sinθ₂) describes the relationship between the angles of incidence and refraction when light crosses the boundary between two media with different refractive indices. When light enters a denser medium (higher n), it bends toward the normal. When it enters a less dense medium, it bends away from the normal.

**Q: What is the refractive index?**

A: The refractive index (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in that material: n = c/v. Higher refractive index means light travels slower in that medium. Air has n ≈ 1.00, water n ≈ 1.33, glass n ≈ 1.52, and diamond n ≈ 2.42.

**Q: What is total internal reflection?**

A: Total internal reflection occurs when light traveling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle. Instead of refracting through, all light is reflected back. This phenomenon is essential for fiber optics, prisms in binoculars, and the sparkle of diamonds.

**Q: How is the critical angle calculated?**

A: The critical angle θc = arcsin(n₂/n₁) exists only when n₁ > n₂ (light going from denser to less dense medium). For glass (n=1.52) to air (n=1.00), the critical angle is about 41.1°. For water to air, it is about 48.8°. At angles above the critical angle, total internal reflection occurs.

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Source: https://vastcalc.com/calculators/physics/snells-law
Category: Physics
Last updated: 2026-04-21