# Snell's Law Calculator

n₁·sinθ₁ = n₂·sinθ₂ for either angle, with the total-internal-reflection regime and critical angle when sinθ exceeds 1.

> Canonical page: https://elysiatools.com/en/tools/snell-law-calculator

- **Category:** Science & Education

- **Keywords:** snells law, refraction, refractive index, total internal reflection, critical angle, optics

## Overview

The Snell's Law Calculator computes the angle of refraction or incidence for light traveling between two optical media using the relationship n₁·sinθ₁ = n₂·sinθ₂. It determines ray deviation relative to the surface normal and identifies total internal reflection boundaries along with the corresponding critical angle.

## Inputs

- **Solve for** (select)
- **Refractive index n₁ (incident side)** (number): e.g. 1.0
- **Refractive index n₂ (refracted side)** (number): e.g. 1.5
- **Given angle (degrees)** (number): e.g. 30

## When to use

- Determining the refracted angle of a light beam crossing an interface between two optical materials.
- Back-calculating the required angle of incidence needed to achieve a target exit angle.
- Evaluating whether an incident ray entering a rarer medium exceeds the critical angle and undergoes total internal reflection.

## How it works

- Select whether to solve for the refraction angle (θ₂) or the incidence angle (θ₁).
- Enter the refractive indices for the incident medium (n₁) and the refracted medium (n₂).
- Specify the known angle value in degrees.
- The calculator applies Snell's law to yield the resulting angle, ray bending behavior, and any critical angle thresholds.

## Use cases

- Verifying theoretical refraction angles and critical limits for physics laboratory coursework.
- Calculating ray deflection angles across air-glass boundaries in lens and prism configurations.
- Assessing core-to-cladding boundary conditions and internal reflection thresholds in optical fiber systems.

## Frequently asked questions

### What is Snell's Law?

Snell's Law describes light refraction at an interface using the formula n₁·sinθ₁ = n₂·sinθ₂, where n represents the refractive index and θ represents the angle to the normal.

### What happens when light exceeds the critical angle?

When light passes from a higher to a lower refractive index (n₁ > n₂) and sinθ₂ exceeds 1, refraction cannot occur and total internal reflection takes place.

### Can I calculate the incident angle instead of the refracted angle?

Yes, choose 'Incidence angle θ₁' under the 'Solve for' setting and enter the known refraction angle.

### How is ray bending direction determined?

Light bends toward the normal when entering an optically denser medium (n₂ > n₁) and away from the normal when entering a rarer medium (n₂ < n₁).

### What units are used for input angles?

All angle inputs and calculation outputs are measured in degrees.

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