Snell's Law Refraction Calculator
Snell's law relates the angles of incidence and refraction when light crosses the boundary between two media, letting you find the bent ray's angle or an unknown refractive index.
Solve for
°
From Snell’s law n₁·sin(θ₁) = n₂·sin(θ₂)
- 1
sin(θ₁)
sin(30°) = 0.5 - 2
Snell ratio n₁·sin(θ₁) ÷ n₂
1 × 0.5 ÷ 1.5 = 0.333333 - 3
Refraction angle θ₂
arcsin(0.333333) = 19.47Arcsine converts the ratio back to an angle in degrees.
How does this calculator work?
Snell's law, n₁·sin(θ₁) = n₂·sin(θ₂), predicts how light bends at a boundary. Given two refractive indices and the incidence angle, the refraction angle is θ₂ = arcsin(n₁·sin(θ₁)/n₂). If that ratio exceeds 1, the light reflects entirely (total internal reflection) instead of refracting.
Formula
How this is calculated
Enter the refractive index of the first medium (n₁, e.g. ~1.00 for air), and either the second index n₂ or the refraction angle θ₂, plus the incidence angle θ₁ measured from the surface normal. Use the selector to choose what to solve for.
When solving for the refraction angle, the calculator computes θ₂ = arcsin(n₁·sin(θ₁) / n₂). Angles are converted between degrees and radians internally. If the dimensionless ratio n₁·sin(θ₁)/n₂ exceeds 1, no real angle exists: the light undergoes total internal reflection and is flagged accordingly. When solving for the second index, it rearranges to n₂ = n₁·sin(θ₁) / sin(θ₂).
Angles are entered in degrees from 0 to 90, and refractive indices are dimensionless values of at least 1 for ordinary transparent media. The law assumes a single planar interface, monochromatic light, and isotropic, non-absorbing media; dispersion (index varying with wavelength) is ignored.
Frequently asked questions
When light travels from a denser to a less dense medium (n₁ > n₂) at a steep enough angle, the computed ratio n₁·sin(θ₁)/n₂ exceeds 1 and no refracted ray exists — all light reflects back. The threshold incidence angle is the critical angle, θc = arcsin(n₂/n₁).
Both the incidence angle θ₁ and refraction angle θ₂ are measured from the normal — the line perpendicular to the surface — not from the surface itself.
Glass has a higher refractive index than air, so light slows down and bends toward the normal (θ₂ < θ₁). Going the other way, into a lower-index medium, it bends away from the normal.
Also known as
TG we-Calculate Editorial Team. (2026). Snell's Law Refraction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/snells-law-calculator
TG we-Calculate Editorial Team. "Snell's Law Refraction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/snells-law-calculator.
TG we-Calculate Editorial Team, "Snell's Law Refraction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/snells-law-calculator
@misc{wecalculate_snells_law_calculator, title = {Snell's Law Refraction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/snells-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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