Snell's Law CalculatorCalculator
Calculate angle of refraction (n1·sin θ1 = n2·sin θ2), critical angle, and total internal reflection (TIR) for optical interfaces.
Optical Interface Media
Refraction & Reflection Results
Snell's Law Calculator - Refraction & Total Internal Reflection: Free Snell. Solve physics equations with formulas and instant scientific calculation. Fast, browser-based, and free. 100% free and private browser utility.
How to Use the Snell's Law Calculator
Define Optical Media Indices
Enter refractive index n1 of incident medium and n2 of refractive medium.
Specify Angle of Incidence (θ1)
Enter the angle between incident light beam and normal surface vector.
Inspect Angle of Refraction (θ2)
Read the refracted angle according to Snell's Law (n1·sin θ1 = n2·sin θ2).
Check Total Internal Reflection (TIR)
Examine critical angle θ_c and determine whether light escapes or reflects 100%.
Physics Principles & Thermodynamics Guide
Snell's Law of Refraction (also known as the Snell-Descartes Law), formulated by Dutch astronomer Willebrord Snellius in 1621, describes the relationship between the angles of incidence and refraction when a wave (such as light or sound) passes through the boundary between two isotropic media with differing refractive indices.
The law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the reciprocal ratio of the indices of refraction: n1 · sin(θ1) = n2 · sin(θ2), where n = c / v is the refractive index representing how much light slows down inside the medium relative to vacuum.
When light travels from an optically less dense medium into a denser medium (n1 < n2, e.g., air into water), light slows down and bends toward the surface normal (θ2 < θ1). Conversely, when light travels from a denser medium into a less dense medium (n1 > n2, e.g., water or glass into air), it speeds up and bends away from the normal (θ2 > θ1).
When traveling from denser to less dense media, there exists a critical angle of incidence θ_c = arcsin(n2 / n1) where the refracted ray would bend to a parallel 90°. If the incidence angle exceeds this critical threshold (θ1 > θ_c), the light cannot escape into the second medium and undergoes Total Internal Reflection (TIR), reflecting 100% of its energy back into the medium. TIR is the foundational physics engine powering modern global fiber optic communications, medical endoscopes, and diamond brilliance.
Key Scientific Advantages
Fiber Optics & Telecommunications
Calculates critical angles enabling 100% light trapping inside glass fiber cores.
Total Internal Reflection Detection
Automatically alerts when angle of incidence exceeds critical angle θ_c.
Lens & Prism Ray Tracing
Computes deviation angles δ = |θ1 - θ2| for optical design and camera lenses.
Light Phase Velocity Sizing
Computes exact propagation speed of light v = c/n inside each optical medium.
Dispersion Modeling
Models chromatic aberration and rainbow refraction across optical frequencies.
Private Optical Engineering
Proprietary prism and waveguide specifications remain 100% confidential.
Frequently Asked Questions
The refractive index n is a dimensionless number that describes how fast light travels through a material: n = c / v, where c is the speed of light in vacuum (≈ 300,000 km/s) and v is phase velocity in the material.
Total Internal Reflection occurs when light traveling in an optically denser medium strikes a boundary with a less dense medium at an angle greater than the critical angle, reflecting 100% of light with zero loss.
Diamond has a very high refractive index (n = 2.417), resulting in an extremely small critical angle of just 24.4°. Light entering a cut diamond undergoes multiple total internal reflections before exiting the top facets.
For water (n = 1.333) to air (n = 1.0003), the critical angle is θ_c = arcsin(1.0003 / 1.333) ≈ 48.6°. Any light striking the water surface at > 48.6° is completely reflected back underwater.
Light rays reflected from the submerged straw bend away from the surface normal as they exit the water into air, causing your eyes to trace them back to a shallower virtual position.