# Critical Angle and Total Internal Reflection Calculator θ_c = arcsin(n₂/n₁) with the Brewster angle — glass 41.81°, diamond 24.44°, the physics of fibers and sparkle. > Canonical page: https://elysiatools.com/en/tools/critical-angle-total-reflection - **Category:** Science & Education - **Keywords:** critical angle, total internal reflection, optical fiber, brewster angle, refractive index, optics ## Overview The Critical Angle and Total Internal Reflection Calculator computes the exact critical angle (θ_c) and Brewster angle (θ_B) between two optical media based on their refractive indices (n₁ and n₂). When light travels from an optically denser medium into a rarer medium, any angle of incidence equal to or exceeding the critical angle causes 100% of the light to reflect back with zero transmission loss. Use this tool to analyze optical fibers, prisms, gem cuts, and polarization boundaries instantly. ## Inputs - **Refractive index n₁ (denser medium)** (number): e.g. 1.5 - **Refractive index n₂ (rarer medium)** (number): e.g. 1.0 ## When to use - Determining the critical angle for light trapping inside fiber optic cores and cladding interfaces. - Designing prism periscopes, binoculars, or internal reflection optics where total reflection replaces silvered mirrors. - Calculating Brewster's angle to find the exact angle for total linear polarization upon reflection. ## How it works - Enter the refractive index of the denser medium (n₁) and the rarer medium (n₂), ensuring n₁ is greater than n₂. - The tool computes the ratio n₂/n₁ and applies the arcsine function (θ_c = arcsin(n₂/n₁)) to determine the critical angle. - It evaluates the arctangent function (θ_B = arctan(n₂/n₁)) to calculate the Brewster polarization angle. - Review the resulting angles in degrees alongside boundary ratio details. ## Use cases - Optical fiber engineering: calculating core-to-cladding acceptance angles to prevent signal leakage. - Gemology and jewelry design: assessing refractive indices to maximize facet light bouncing and dispersion. - Physics education: demonstrating Snell's law limits, refraction cutoffs, and polarization principles. ## Frequently asked questions ### What is a critical angle? The critical angle is the minimum angle of incidence at which light traveling from a denser medium to a rarer medium undergoes total internal reflection instead of refracting. ### Why must n₁ be greater than n₂? Total internal reflection only occurs when light moves from an optically denser medium into an optically rarer medium; if n₁ ≤ n₂, sin(θ_c) exceeds 1 and no critical angle exists. ### What is the Brewster angle output? The Brewster angle (θ_B = arctan(n₂/n₁)) is the angle of incidence at which light with p-polarization is perfectly transmitted, leaving reflected light 100% s-polarized. ### Does light lose energy during total internal reflection? No, total internal reflection reflects 100% of the optical power at the boundary with zero transmission loss. ### Can I calculate the critical angle for water and air? Yes, enter 1.333 for water (n₁) and 1.000 for air (n₂) to obtain the critical angle of approximately 48.61°. ## Related tools - [Gravitational Time Dilation Calculator](https://elysiatools.com/en/tools/gravitational-time-dilation): dτ = dt·√(1 − 2GM/(rc²)) for Earth, Sun, or custom mass: Schwarzschild radius, dilation factor, and daily/yearly clock lag outside the horizon. - [Half-Life by Reaction Order](https://elysiatools.com/en/tools/half-life-reaction-order): t½ = a₀/(2k), ln 2/k or 1/(k·a₀) for zero-, first- and second-order reactions, with timelines and depletion time. - [Linear Programming Simplex Solver (Two-Phase)](https://elysiatools.com/en/tools/linear-programming-simplex): Two-phase simplex for 2–6 variables and 1–8 ≤/≥/= constraints: Bland's rule, per-iteration pivot log, optimal/unbounded/infeasible status, and substitution checks. - [Daily Compound Interest Calculator](https://elysiatools.com/en/tools/compound-interest-daily): Calculate compound interest with daily compounding for savings and investments - [Credit Card Payoff Calculator](https://elysiatools.com/en/tools/credit-card-payoff): Compare avalanche (highest APR first) vs snowball (lowest balance first) strategies for paying off multiple credit cards. 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