Critical Angle Calculator (Optics)

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

Use the Critical Angle Calculator (Optics)

Refractive Indices

Glass ≈ 1.5  |  Diamond ≈ 2.417  |  Water ≈ 1.333

Air ≈ 1.0  |  Water ≈ 1.333  |  Glass ≈ 1.5

Common presets

Enter refractive indices and press Calculate.

Summary

The critical angle is the minimum angle of incidence (measured from the normal) at which light traveling from a denser to a less dense medium undergoes total internal reflection (TIR) instead of refracting out. It is derived from Snell's law by setting the refracted angle to 90°, giving θ_c = arcsin(n₂ / n₁). This tool computes that angle instantly and lets you check whether a given angle of incidence will produce TIR.

How it works

  1. Enter the refractive index of the incident medium (n₁ — must be greater than n₂ for TIR to be possible).
  2. Enter the refractive index of the second medium (n₂).
  3. The tool applies θ_c = arcsin(n₂ / n₁) to compute the critical angle.
  4. Optionally enter an angle of incidence to see whether TIR occurs (angle ≥ θ_c) or whether light refracts (angle < θ_c).
  5. 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: 2026-06-13 · Reviewed by Nham Vu