What is total internal reflection?

When light travels from a denser medium (higher n) to a less dense medium (lower n) and hits the boundary at an angle equal to or greater than the critical angle, all light is reflected back — none passes through. This is total internal reflection.

What is the critical angle formula?

θc = arcsin(n2 / n1), where n1 is the refractive index of the incident medium and n2 is the refractive index of the second medium. TIR only exists when n1 > n2.

Why must n1 be greater than n2?

TIR can only happen when light moves from a denser to a less dense medium. If n1 ≤ n2, light bends toward the normal at the boundary and there is no critical angle.

What is the critical angle for water to air?

Water has n ≈ 1.333 and air has n ≈ 1.000, giving a critical angle of arcsin(1/1.333) ≈ 48.75°. Light hitting a water surface from below at more than ~49° is totally reflected.

How does refractive index affect the critical angle?

A higher ratio n2/n1 pushes the critical angle closer to 90°, meaning TIR only occurs at very steep angles. A lower ratio (large contrast between media) yields a smaller critical angle, making TIR easier to achieve.

Can I use this for glass-to-air interfaces?

Yes. Common glass has n ≈ 1.5, so the glass-to-air critical angle is arcsin(1/1.5) ≈ 41.8°. Enter n1 = 1.5 and n2 = 1.0 to confirm.

Total Internal Reflection Calculator

Name: Total Internal Reflection Calculator
Availability: InStock
Author: Nham Vu

Enter the refractive indices of two media to compute the critical angle for total internal reflection.

Refractive Indices

n₁ — Incident medium (denser)

Examples: glass 1.5, water 1.333, diamond 2.417

n₂ — Second medium (less dense)

Examples: air 1.000, water 1.333, glass 1.5

Angle of incidence: 45°

0°90°

Preset pairs

Critical Angle

Formula Breakdown

n₁ (incident)—

n₂ (second)—

n₂ / n₁—

arcsin(ratio)—

θ_c—

Ray Diagram

Adjust inputs to see ray behavior

Summary

Enter the refractive indices of two media to compute the critical angle for total internal reflection.

How it works

Enter the refractive index of the first (denser) medium (n1).
Enter the refractive index of the second (less dense) medium (n2).
The calculator applies Snell's law at 90°: θc = arcsin(n2 / n1).
The critical angle and a summary of the TIR condition are displayed instantly.
Use the angle-of-incidence slider to visualize whether TIR occurs for a given ray.

Use cases

Designing fiber-optic cables where light must stay trapped in the core.
Understanding why diamonds sparkle (high refractive index raises TIR efficiency).
Calculating the critical angle for a water-air interface in pool/aquarium optics.
Teaching Snell's law and TIR in undergraduate physics labs.
Selecting glass types for total-internal-reflection prisms in binoculars.
Checking whether a given angle of incidence will produce TIR for a specific material pair.

Frequently Asked Questions

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