Snell's Law describes how light bends when passing from one medium to another. It states that n1·sin(θ1) = n2·sin(θ2), where n1 and n2 are the refractive indices of the two media and θ1, θ2 are the angles measured from the normal to the interface.

What is total internal reflection?

When light travels from a denser medium to a less dense medium (higher n to lower n) and the incident angle exceeds the critical angle, all light is reflected back into the first medium — none passes through. This is total internal reflection, and it is the principle behind fiber optic cables.

What is the refractive index?

The refractive index (n) is the ratio of the speed of light in a vacuum to the speed of light in a given medium. Air ≈ 1.000, water ≈ 1.333, standard glass ≈ 1.520, and diamond ≈ 2.417.

Why are angles measured from the normal?

Optics conventions measure angles relative to the normal (a line perpendicular to the surface at the point of incidence), not the surface itself. This makes Snell's Law consistent for any orientation of the interface.

What does an incident angle of 0° mean?

An incident angle of 0° means light hits the surface straight on (perpendicular). In this case sin(0°) = 0, so the refracted angle is also 0° — light passes straight through without bending regardless of the media.

Snell's Law Refraction Calculator

Enter the incident angle and refractive indices of two media to calculate the refracted angle using Snell's Law.

Inputs

Incident Angle (θ₁)

degrees

Medium 1 (incident)

Medium 2 (refracted)

Refracted Angle (θ₂)

—

Critical Angle

—

for total internal reflection

n1 · sin θ₁

—

must equal n2 · sin θ₂

Ray Diagram

Formula: n₁ · sin(θ₁) = n₂ · sin(θ₂) → θ₂ = arcsin(n₁/n₂ · sin(θ₁))

Summary

Enter the incident angle and refractive indices of two media to calculate the refracted angle using Snell's Law.

How it works

Enter the incident angle (the angle between the incoming ray and the normal to the surface).
Select or enter the refractive index for Medium 1 (where light originates).
Select or enter the refractive index for Medium 2 (where light enters).
The calculator applies Snell's Law: n1·sin(θ1) = n2·sin(θ2).
The refracted angle θ2 is displayed, along with total internal reflection detection.

Use cases

Calculate the bending angle of light entering water from air.
Determine the critical angle for total internal reflection in fiber optics.
Design optical elements like lenses, prisms, and waveguides.
Verify ray-tracing calculations in optics coursework.
Understand why objects appear displaced when viewed through glass or water.
Model light behavior at the interface of any two transparent media.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu