Critical Angle Calculator

The critical angle is the minimum angle of incidence — measured from the normal — at which total internal reflection occurs. When light travels from a denser medium (higher refractive index) to a less dense medium (lower refractive index) at exactly the critical angle, the refracted ray travels along the boundary at 90°. Any incident angle greater than the critical angle results in total internal reflection with no refracted ray.

The critical angle θc is calculated using: θc = 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 it's entering. This formula is derived from Snell's Law (n₁·sin θ₁ = n₂·sin θ₂) by setting the refraction angle θ₂ to 90°.

Snell's Law states that n₁·sin(θ₁) = n₂·sin(θ₂), describing how light bends when passing between two media with different refractive indices. The critical angle is a special case of Snell's Law: when the refracted angle θ₂ equals 90°, sin(90°) = 1, so the equation simplifies to sin(θc) = n₂/n₁. Beyond this angle, no refraction occurs and all light is reflected back into the original medium.

Total internal reflection is only possible when light travels from a medium with a higher refractive index to one with a lower refractive index (n₁ > n₂). For example, light going from glass (n≈1.5) to air (n≈1.0) can undergo TIR, but light going from air to glass cannot. Additionally, the angle of incidence must meet or exceed the critical angle.

For common glass (n₁ ≈ 1.5) to air (n₂ ≈ 1.0), the critical angle is approximately 41.8°. This means any light ray inside the glass hitting the glass-air boundary at an angle greater than 41.8° (from the normal) will be totally internally reflected. This property is exploited in optical fibers and prismatic binoculars.

Yes, Snell's Law applies to any wave that changes speed at a boundary — including sound waves, seismic waves, and electromagnetic waves (light, radio waves, etc.). However, the critical angle calculator here is specifically designed for light, using optical refractive indices. For other wave types, the equivalent ratio of wave speeds in each medium would replace n₂/n₁.

Some common refractive indices include: Vacuum = 1.000 (exact), Air ≈ 1.0003, Water ≈ 1.333, Ice ≈ 1.309, Ethanol ≈ 1.36, Acrylic/Plexiglass ≈ 1.49, Standard glass ≈ 1.5, Flint glass ≈ 1.66, and Diamond ≈ 2.417. Higher refractive index means light travels more slowly in that medium. Use the quick-pick dropdowns above to auto-fill these values.

Total internal reflection — and thus a critical angle — only exists when n₁ > n₂ (light going from denser to less dense medium). If you enter n₁ ≤ n₂, the ratio n₂/n₁ ≥ 1, and arcsin of a value ≥ 1 is undefined (no real angle). In this case, the calculator flags that TIR is not possible. Swap your n₁ and n₂ values if you intended the reverse direction of travel.