Ângulo Limite (Refl. Total)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
refl. total interna
About this calculator
The critical angle calculator determines the maximum angle of incidence for which total internal reflection occurs at an interface between two media. This optical phenomenon happens when light travels from a denser medium (higher refractive index) to a rarer medium (lower index). The critical angle is given by Snell's law: sin θ_c = n₂ / n₁, where n₁ is the index of the incident medium and n₂ of the refracting medium. Total internal reflection only occurs if n₁ > n₂.
The calculator works simply: you enter the refractive indices of the two media (n₁ and n₂), and it computes the critical angle in degrees. For example, for water (n₁ = 1.33) and air (n₂ = 1.00), the critical angle is about 48.6°. Any incident angle larger than this results in total reflection, with no refraction. This tool is useful for students and professionals in optics, engineering, and physics.
When to use? In fiber optic design, where light must be confined in the core by total internal reflection. Also in teaching labs to demonstrate the phenomenon, or when designing prisms and optical sensors. Cautions: ensure n₁ > n₂, otherwise there is no critical angle (total internal reflection does not occur). Additionally, the calculator assumes isotropic and homogeneous media; for anisotropic or absorbing media, results may differ.
Frequently asked questions
What is total internal reflection?
It is an optical phenomenon where light incident on an interface between two media is completely reflected back into the original medium, with no refraction. It occurs when the angle of incidence is greater than the critical angle and the incident medium has a higher index.
Why does the critical angle exist only if n₁ > n₂?
From Snell's law, sin θ_c = n₂/n₁. If n₁ ≤ n₂, the ratio is ≥ 1, and there is no real angle whose sine is greater than 1, so no critical angle exists and total internal reflection cannot occur.
How to calculate the critical angle manually?
Use the formula sin θ_c = n₂/n₁. First divide the smaller index by the larger, then apply the arcsine function (sin⁻¹) to the result. The angle will be in radians; convert to degrees by multiplying by 180/π.
Does the calculator work for media like glass and diamond?
Yes, as long as you enter the correct indices. For example, glass (n≈1.5) and air (n=1) give a critical angle ≈ 41.8°. For diamond (n≈2.42) and air, the angle is ≈ 24.4°.
What is the most common practical application of total internal reflection?
Optical fibers: light travels through the fiber core undergoing multiple total internal reflections at the walls, enabling data transmission over long distances with low loss.