Snell's Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
Snell's law gives n₁sin(θ₁) = n₂sin(θ₂). For a ray passing from air (n=1) to water (n=1.33) with an angle of incidence of 30°, the angle of refraction is about 22.08°, the ray bending closer to the normal as it enters the denser medium.
Explanation
Snell's law describes how a light ray changes direction when passing from one transparent medium to another (from air to water, from air to glass): this change in the speed of light depending on each medium's refractive index (see our refractive index calculator for that speed) causes its path to bend at the interface, unless the ray arrives perpendicular to the surface. The general rule is intuitive once stated: when passing from an optically less dense medium (lower index, like air) into a denser one (higher index, like water or glass), the ray bends closer to the normal (the refraction angle is smaller than the incidence angle) — this is the phenomenon that explains why a stick dipped in water appears "broken" at the surface. In the opposite direction (from a denser medium to a less dense one), the ray bends away from the normal, and beyond a certain incidence angle called the critical angle, a phenomenon called total internal reflection occurs: light no longer crosses the interface, it is entirely reflected back inside the denser medium, a principle notably exploited in optical fiber to guide light over long distances with minimal loss. This same change of speed while crossing a medium shows up, in another form, in our Doppler effect calculator, where it's the relative speed of the source with respect to the observer that shifts the perceived frequency rather than the ray's path.
Example: a ray passing from air to water, 30° angle of incidence
Inputs
Medium 1 index (air): 1. Angle of incidence: 30°. Medium 2 index (water): 1.33.
Calculation
sin(θ₂) = (1 × sin(30°)) ÷ 1.33 = 0.5 ÷ 1.33 ≈ 0.3759. θ₂ = arcsin(0.3759) ≈ 22.08°.
Result
The ray bends to about 22.08° from the normal upon entering the water, closer to perpendicular than its 30° angle of incidence.
Frequently asked questions
Why does a stick dipped in water appear broken?
Because the light reflected off the submerged part of the stick is bent as it crosses the water-air interface before reaching the observer's eye, exactly as described by Snell's law. The brain interprets this light assuming it traveled in a straight line, which creates the visual illusion of a discontinuity at the water's surface, even though the stick itself is perfectly straight.
What is the critical angle and total internal reflection?
The critical angle is the angle of incidence, reached only when passing from a denser medium to a less dense one, beyond which light can no longer cross the interface and is entirely reflected back inside the original medium. This calculator illustrates this limit: if the calculated refraction angle would require an arcsine of a value greater than 1 (mathematically impossible), that's the sign the critical angle has been exceeded and total internal reflection occurs instead of refraction.
Does this law apply the same way to all colors of light?
Not quite: a material's refractive index varies slightly with the wavelength (color) of light, a phenomenon called dispersion. This dependency is what explains white light splitting into a rainbow of colors through a prism, each color bending at a slightly different angle. This calculator uses a single refractive index, an approximation valid for a given wavelength.