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Snell's Law of Refraction

Also known as law of refraction · n₁sinθ₁ = n₂sinθ₂

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2
sig figs

Worked example: Air to glass at 30 deg → theta2 = arcsin(1/3) = 19.4712 deg. Press Try an example to run it live, then adjust anything.

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Where Snell's Law of Refraction fits

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Your answer feeds
Apparent DepthCritical Angle for Total Internal ReflectionBrewster's AngleThin-Film Constructive Interference (Bright Reflection)
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See also

Apparent Depth: Both use index of refraction.Brewster's Angle: Both use index of refraction.Critical Angle for Total Internal Reflection: Both use index of refraction.Index of Refraction (n = c/v): Both use index of refraction.Thin-Film Constructive Interference (Bright Reflection): Both use index of refraction.Thin-Film Destructive Interference (Dark Reflection): Both use index of refraction.
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Snell's Law of Refraction explained

θ1θ2n1n2

Light crossing into a denser medium slows down, and to keep its wavefronts connected it must bend toward the normal: by exactly the amount that keeps n sin θ constant. A ray entering water (n = 1.333) from air at 45° refracts to arcsin(sin 45°/1.333) ≈ 32°, which is why a pool's floor looks shallower than it is and a straw appears kinked at the surface.

Run the light the other way, from dense to thin, and Snell's law eventually fails to give an answer: past the critical angle the sine would exceed 1 and the ray reflects totally instead, the trick that traps light inside optical fibers.

Snell's Law of Refraction formula

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2
Where
  • n1n_1= Index of refraction (medium 1)
  • θ1\theta_1= Angle of incidence (°)
  • n2n_2= Index of refraction (medium 2)
  • θ2\theta_2= Angle of refraction (°)
In this toolkit

Refraction and total internal reflection

5 formulasSnell's law and the refractive index, with the critical angle, Brewster's angle and apparent depth that follow from bending light at a boundary.

Revised 31 October 2026
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formula.expert. (2026, October 31). Snell's Law of Refraction Formula & Calculator. https://formula.expert/solvers/snells-law

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