What is the critical angle?

The critical angle is the angle of incidence (measured from the normal) above which light traveling from a denser to a less dense medium undergoes total internal reflection instead of passing through the boundary.

What formula is used?

The critical angle θ_c is given by θ_c = arcsin(n2 / n1), where n1 is the refractive index of the medium the light is coming from and n2 is the refractive index of the medium the light would enter.

Why must n1 be greater than n2?

Total internal reflection only occurs when light moves from a denser medium to a less dense medium (n1 > n2). If n1 ≤ n2, no critical angle exists because refraction always occurs at any angle of incidence.

What is the critical angle for glass and air?

For typical glass (n1 ≈ 1.5) in air (n2 = 1.0), the critical angle is arcsin(1.0 / 1.5) ≈ 41.8°. This is why optical fibers can guide light with minimal loss.

What happens at the critical angle exactly?

At exactly the critical angle, the refracted ray travels along the boundary (90° from the normal). Above this angle, the light is totally internally reflected.

What are typical refractive indices?

Vacuum: 1.0, Air: ~1.0003, Water: ~1.333, Crown glass: ~1.52, Diamond: ~2.417. The tool provides common presets for convenience.

Is the critical angle always 42 degrees?

No. About 42° is the value for a typical glass-to-air boundary (n1 ≈ 1.5). The critical angle changes with the media: water-to-air is about 48.6°, and diamond-to-air is only about 24.4°. Always compute it from the actual refractive indices.

Critical Angle Calculator

Name: Critical Angle Calculator
Availability: InStock
Author: Nham Vu

Enter two refractive indices to instantly calculate the critical angle for total internal reflection.

Refractive Indices

Common Presets

n₁ — Refractive index of the denser medium

Must be greater than n₂

n₂ — Refractive index of the less dense medium

Result

Enter refractive indices and press Calculate.

Copied!

Summary

Enter two refractive indices to instantly calculate the critical angle for total internal reflection.

How it works

Enter the refractive index of the denser medium (n1) in the first field.
Enter the refractive index of the less dense medium (n2) in the second field.
The tool applies the formula θ_c = arcsin(n2 / n1) to compute the critical angle.
Results are displayed in both degrees and radians.
Use the preset buttons to load common material pairs instantly.

Use cases

Physics students verifying Snell's law problems for total internal reflection.
Optical engineers designing fiber-optic cables and waveguides.
Photographers understanding why underwater scenes exhibit total internal reflection.
Gemologists calculating TIR angles for diamond and gemstone cuts.
Teachers preparing demonstrations of light behavior at medium boundaries.
Researchers studying prism-based optical instruments.

Frequently Asked Questions

Related tools

Snells Law Calculator Refractive Index Calculator Wavelength Calculator

Last updated: 2026-05-23 · Reviewed by Nham Vu