What is the critical angle?

It is the angle of incidence (from the normal) at which the refracted ray runs exactly along the interface (90°). Any incidence angle greater than this results in total internal reflection — no light passes into the second medium.

Why must n₁ be greater than n₂?

TIR only occurs when light moves from a denser to a less dense medium. If n₁ ≤ n₂, arcsin(n₂/n₁) is undefined (ratio > 1), so there is no critical angle and light always refracts.

What is the critical angle for glass to air?

For standard glass (n₁ ≈ 1.5) going to air (n₂ = 1.0), θ_c = arcsin(1/1.5) ≈ 41.8°. Any light hitting the interface above this angle reflects completely.

What is the critical angle for water to air?

Water has n₁ ≈ 1.333. The critical angle is arcsin(1/1.333) ≈ 48.6°. This is why objects underwater look distorted when viewed at a shallow angle.

Does the wavelength of light affect the critical angle?

Yes. Refractive index varies with wavelength (dispersion), so different colors have slightly different critical angles. This tool uses single-value refractive indices for simplicity.

Critical Angle Calculator (Optics)

Name: Critical Angle Calculator (Optics)
Availability: InStock
Author: Nham Vu

Enter two refractive indices to find the critical angle for total internal reflection, and check any incidence angle against that threshold.

Refractive Indices

n₁ — Incident medium (denser)

Glass ≈ 1.5 | Diamond ≈ 2.417 | Water ≈ 1.333

n₂ — Second medium (less dense)

Air ≈ 1.0 | Water ≈ 1.333 | Glass ≈ 1.5

Common presets

Check angle of incidence (optional, °)

Enter refractive indices and press Calculate.

Summary

Enter two refractive indices to find the critical angle for total internal reflection, and check any incidence angle against that threshold.

How it works

Enter the refractive index of the incident medium (n₁ — must be greater than n₂ for TIR to be possible).
Enter the refractive index of the second medium (n₂).
The tool applies θ_c = arcsin(n₂ / n₁) to compute the critical angle.
Optionally enter an angle of incidence to see whether TIR occurs (angle ≥ θ_c) or whether light refracts (angle < θ_c).
The refracted angle for non-TIR cases is also shown via Snell's law: n₁ sin θ_i = n₂ sin θ_r.

Use cases

Designing optical fibers where light must stay trapped by TIR.
Understanding why diamonds sparkle — high refractive index creates a small critical angle.
Analyzing prism-based periscopes and retroreflectors.
Checking whether a glass-to-air interface will reflect laser beams.
Physics homework involving Snell's law and TIR problems.
Verifying critical angles for common materials like glass, water, and diamond.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu