Snell's Law Calculator
Use Snell's law to find the angle of refraction when light passes between two media, and detect total internal reflection.
How it works
n₁ × sin θ₁ = n₂ × sin θ₂ · sin θ₂ = n₁ sin θ₁ / n₂
Snell's law describes how light bends when it crosses from one medium into another. The refractive index n measures how much a medium slows light. Rearranging gives the sine of the refraction angle; taking the inverse sine returns the angle. When that sine exceeds 1 the light cannot escape and totally internally reflects instead.
Worked example
Light hitting water (n₂ = 1.33) from air (n₁ = 1.0) at 30° refracts to θ₂ = arcsin((1.0 × sin30°) ÷ 1.33) ≈ 22.1°, bending toward the normal.
Frequently asked questions
What is total internal reflection?
When light travels from a denser to a lighter medium beyond a critical angle, none of it refracts out — it all reflects back inside. This is how optical fibres trap light.
What is a refractive index?
It is the ratio of the speed of light in a vacuum to its speed in the medium. Air is about 1.00, water 1.33 and glass roughly 1.5.
Why does light bend at all?
It changes speed when entering a new medium. That change of speed at the boundary redirects the wavefronts, which we see as bending.
Related calculators
Educational estimate. Check the formula and units for your exact case.