Snell's Law 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 the light ray makes with the normal to the interface. It describes how light (or any wave) bends when crossing a boundary between media with different optical densities.

What is a refractive index?

The refractive index (n) of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. Vacuum has n = 1.000; air is approximately 1.000293; water is about 1.333; glass ranges from 1.5 to 1.9 depending on type; diamond is 2.417.

What is total internal reflection?

When light travels from a denser medium (higher n) to a less dense medium (lower n) and the angle of incidence exceeds the critical angle, all light is reflected back — none is transmitted. The critical angle θc = arcsin(n2/n1). This principle is exploited in optical fiber and prism binoculars.

Why does the calculator show "Total Internal Reflection"?

This appears when the computed value of (n1/n2)·sin(θ1) exceeds 1, which has no real arcsin solution. It means the light cannot exit into the second medium at that angle — it is entirely reflected back into the first medium.

Can I calculate the refractive index instead of an angle?

Currently the calculator solves for the unknown angle. To find a refractive index, rearrange the formula: n2 = n1·sin(θ1)/sin(θ2). You can do this manually once you have the angles, or use the formula directly.

Are the angles measured from the normal or the surface?

All angles in this calculator and in the standard form of Snell's Law are measured from the normal — the line perpendicular to the interface at the point of incidence. An angle of 0° means the light hits the surface straight on (perpendicularly).

Snell's Law Calculator

Enter two refractive indices and one angle to instantly compute the missing angle using Snell's Law.

Input Parameters

Medium 1 — Refractive Index (n₁)

Angle of Incidence (θ₁) — degrees

Medium 2 — Refractive Index (n₂)

Angle of Refraction (θ₂) — degrees (leave blank to calculate)

Common Refractive Indices

Medium	n
Vacuum	1.000
Air	1.000293
Water (20 °C)	1.333
Mineral oil	1.474
Crown glass	1.500
Flint glass	1.620
Dense flint glass	1.900
Diamond	2.417

Result

Fill in the fields and click Calculate to see results.

Ray Diagram

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Summary

Snell's Law describes how light bends when it passes from one transparent medium into another. The relationship n1·sin(θ1) = n2·sin(θ2) links the refractive indices of both media to the angles the light ray makes with the normal at the interface. This calculator lets you solve for the unknown angle of incidence or angle of refraction given both media refractive indices and one angle.

How it works

Select or type the refractive index for the first medium (n1).
Select or type the refractive index for the second medium (n2).
Enter the angle of incidence (θ1) or angle of refraction (θ2) in degrees.
Click Calculate to apply n1·sin(θ1) = n2·sin(θ2) and see the missing value.
Use the diagram to visualize the refracted ray at the interface.
Swap the media direction with the Swap button to reverse the calculation.

Use cases

Solve optics homework and exam problems involving light refraction.
Design lenses and prisms for cameras, telescopes, and microscopes.
Calculate the critical angle for total internal reflection in fiber optics.
Verify laboratory measurements of refractive index.
Teach and visualize Snell's Law interactively in a classroom setting.
Check ray-tracing calculations during optical system design.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu